First Summative Test Q1 Interactive Worksheet - Edform - Free Printable
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Step-by-step solution for: First Summative Test Q1 Interactive Worksheet - Edform
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Show Answer Key & Explanations
Step-by-step solution for: First Summative Test Q1 Interactive Worksheet - Edform
Let's solve each question one by one and provide explanations.
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1. What is the next number in the sequence 36, 30, 24, 18, ...?
- The pattern: Each term decreases by 6.
- 36 → 30 (−6)
- 30 → 24 (−6)
- 24 → 18 (−6)
- So, 18 − 6 = 12
- ✔ Answer: a. 12
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2. What is the nth term of the sequence 11, 16, 21, 26, ...?
- This is an arithmetic sequence:
- First term $ a_1 = 11 $
- Common difference $ d = 5 $
- General formula: $ a_n = a_1 + (n-1)d $
- $ a_n = 11 + (n-1)(5) = 11 + 5n - 5 = 5n + 6 $
- ✔ Answer: c. $ a_n = 5n + 6 $
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3. What is the 8th term of the sequence $ a_n = 6n - 7 $?
- Plug in $ n = 8 $:
- $ a_8 = 6(8) - 7 = 48 - 7 = 41 $
- ✔ Answer: d. 41
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4. If the terms of an arithmetic sequence are in increasing order, then the common difference is
- In an increasing sequence, each term is larger than the previous.
- So the common difference must be positive.
- ✔ Answer: a. positive
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5. Which of these expressions represents the fourth term of an arithmetic sequence?
- General formula: $ a_n = a_1 + (n-1)d $
- For $ n = 4 $: $ a_4 = a_1 + 3d $
- ✔ Answer: d. $ a_1 + 3d $
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6. Which of the following describes an arithmetic sequence?
- An arithmetic sequence has a constant difference between terms, so its general form is linear: $ a_n = a_1 + (n-1)d $
- Let’s check each option:
- a. $ a_n = 6n^2 $ → quadratic → not arithmetic
- b. $ a_n = 6n $ → linear → yes! This is arithmetic with $ a_1 = 6 $, $ d = 6 $
- c. $ a_n = \frac{1}{6n} $ → reciprocal → not arithmetic
- d. $ a_n = 6^n $ → exponential → geometric
- ✔ Answer: b. $ a_n = 6n $
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7. Which of these words has the same meaning as arithmetic mean?
- Arithmetic mean = average of numbers
- ✔ Answer: c. average
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8. A term that is between two terms of an arithmetic sequence is called an arithmetic _________.
- Such a term is called an arithmetic mean.
- Example: Between 2 and 6, the arithmetic mean is 4.
- ✔ Answer: d. mean
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9. How many arithmetic means may be inserted between two terms of an arithmetic sequence?
- You can insert any number of arithmetic means between two terms.
- E.g., between 2 and 10, you can insert 1, 2, ..., 9 arithmetic means.
- ✔ Answer: c. any number
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10. Which of the following values cannot be a common ratio of a geometric sequence?
- Common ratio $ r $ can be any real number except zero? Wait — actually:
- $ r = 0 $: Then after first term, all terms become 0 → valid but degenerate.
- But if $ r = 0 $, and $ a_1 = 5 $, then sequence is 5, 0, 0, 0, ...
- Still considered geometric.
- However, if $ r = 0 $, it's not meaningful to have a ratio from second term onward because division by zero is undefined.
- But technically, r = 0 is allowed in some definitions.
- But let's think: Is $ r = 0 $ acceptable?
- Yes, but only if the first term is non-zero.
- However, in most contexts, $ r = 0 $ is not allowed because it makes the sequence collapse.
- But look at the options: c. 0
- Actually, r = 0 is not acceptable because:
- $ a_2 = a_1 \cdot r = 0 $
- $ a_3 = a_2 \cdot r = 0 \cdot 0 = 0 $
- So ratio $ \frac{a_3}{a_2} = \frac{0}{0} $ → undefined!
- So common ratio cannot be 0 because it leads to undefined ratios.
- ✔ Answer: c. 0
---
11. Which of the following is a geometric sequence?
Check each:
a. 3, 7, 11, 15 → differences: +4 → arithmetic, not geometric
b. $ \frac{1}{2}, \frac{1}{3}, \frac{2}{9}, \dots $
- Check ratios:
- $ \frac{1/3}{1/2} = \frac{2}{3} $
- $ \frac{2/9}{1/3} = \frac{2}{9} \cdot 3 = \frac{2}{3} $
- Ratio = $ \frac{2}{3} $ → constant
- ✔ Geometric!
c. 4, 4.5, 5 → differences: +0.5 → arithmetic
d. 2, 3, 5, 8 → no clear ratio or difference → neither
- ✔ Answer: b. $ \frac{1}{2}, \frac{1}{3}, \frac{2}{9}, \dots $
---
12. What is the common ratio of the sequence whose first term and third terms are 2 and 32, respectively?
- Let $ a_1 = 2 $, $ a_3 = 32 $
- In geometric sequence: $ a_3 = a_1 \cdot r^2 $
- $ 32 = 2 \cdot r^2 $
- $ r^2 = 16 $
- $ r = \pm 4 $
- ✔ Answer: b. ±4
---
13. An arithmetic sequence has a common difference while a geometric sequence has a common _________.
- Geometric sequences have a common ratio.
- ✔ Answer: c. ratio
---
14. Which of the following is an arithmetic sequence?
Check each:
a. $ \frac{1}{2}, 1, \frac{3}{2}, \dots $
- Differences: $ 1 - 0.5 = 0.5 $, $ 1.5 - 1 = 0.5 $ → constant → yes
- ✔ Arithmetic
b. 1, -1, 1, -1 → alternates → not arithmetic
c. $ \frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \dots $ → halving → geometric
d. -2, 4, -8 → ratios: $ 4 / (-2) = -2 $, $ -8 / 4 = -2 $ → geometric
- ✔ Answer: a. $ \frac{1}{2}, 1, \frac{3}{2}, \dots $
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15. Which of these is a geometric sequence?
a. 2, 5, 8, 11 → differences: +3 → arithmetic
b. 1, 0, 0, 0 → ratios: $ 0/1 = 0 $, $ 0/0 $ → undefined → not geometric
c. -2, 4, -8 → ratio: $ 4 / (-2) = -2 $, $ -8 / 4 = -2 $ → common ratio = -2 → geometric
d. -2, -4, -6 → differences: -2 → arithmetic
- ✔ Answer: c. -2, 4, -8, ...
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| Q# | Answer |
|----|--------|
| 1 | a. 12 |
| 2 | c. $ a_n = 5n + 6 $ |
| 3 | d. 41 |
| 4 | a. positive |
| 5 | d. $ a_1 + 3d $ |
| 6 | b. $ a_n = 6n $ |
| 7 | c. average |
| 8 | d. mean |
| 9 | c. any number |
|10 | c. 0 |
|11 | b. $ \frac{1}{2}, \frac{1}{3}, \frac{2}{9}, \dots $ |
|12 | b. ±4 |
|13 | c. ratio |
|14 | a. $ \frac{1}{2}, 1, \frac{3}{2}, \dots $ |
|15 | c. -2, 4, -8, ... |
Let me know if you'd like this formatted as a printable answer key!
---
1. What is the next number in the sequence 36, 30, 24, 18, ...?
- The pattern: Each term decreases by 6.
- 36 → 30 (−6)
- 30 → 24 (−6)
- 24 → 18 (−6)
- So, 18 − 6 = 12
- ✔ Answer: a. 12
---
2. What is the nth term of the sequence 11, 16, 21, 26, ...?
- This is an arithmetic sequence:
- First term $ a_1 = 11 $
- Common difference $ d = 5 $
- General formula: $ a_n = a_1 + (n-1)d $
- $ a_n = 11 + (n-1)(5) = 11 + 5n - 5 = 5n + 6 $
- ✔ Answer: c. $ a_n = 5n + 6 $
---
3. What is the 8th term of the sequence $ a_n = 6n - 7 $?
- Plug in $ n = 8 $:
- $ a_8 = 6(8) - 7 = 48 - 7 = 41 $
- ✔ Answer: d. 41
---
4. If the terms of an arithmetic sequence are in increasing order, then the common difference is
- In an increasing sequence, each term is larger than the previous.
- So the common difference must be positive.
- ✔ Answer: a. positive
---
5. Which of these expressions represents the fourth term of an arithmetic sequence?
- General formula: $ a_n = a_1 + (n-1)d $
- For $ n = 4 $: $ a_4 = a_1 + 3d $
- ✔ Answer: d. $ a_1 + 3d $
---
6. Which of the following describes an arithmetic sequence?
- An arithmetic sequence has a constant difference between terms, so its general form is linear: $ a_n = a_1 + (n-1)d $
- Let’s check each option:
- a. $ a_n = 6n^2 $ → quadratic → not arithmetic
- b. $ a_n = 6n $ → linear → yes! This is arithmetic with $ a_1 = 6 $, $ d = 6 $
- c. $ a_n = \frac{1}{6n} $ → reciprocal → not arithmetic
- d. $ a_n = 6^n $ → exponential → geometric
- ✔ Answer: b. $ a_n = 6n $
---
7. Which of these words has the same meaning as arithmetic mean?
- Arithmetic mean = average of numbers
- ✔ Answer: c. average
---
8. A term that is between two terms of an arithmetic sequence is called an arithmetic _________.
- Such a term is called an arithmetic mean.
- Example: Between 2 and 6, the arithmetic mean is 4.
- ✔ Answer: d. mean
---
9. How many arithmetic means may be inserted between two terms of an arithmetic sequence?
- You can insert any number of arithmetic means between two terms.
- E.g., between 2 and 10, you can insert 1, 2, ..., 9 arithmetic means.
- ✔ Answer: c. any number
---
10. Which of the following values cannot be a common ratio of a geometric sequence?
- Common ratio $ r $ can be any real number except zero? Wait — actually:
- $ r = 0 $: Then after first term, all terms become 0 → valid but degenerate.
- But if $ r = 0 $, and $ a_1 = 5 $, then sequence is 5, 0, 0, 0, ...
- Still considered geometric.
- However, if $ r = 0 $, it's not meaningful to have a ratio from second term onward because division by zero is undefined.
- But technically, r = 0 is allowed in some definitions.
- But let's think: Is $ r = 0 $ acceptable?
- Yes, but only if the first term is non-zero.
- However, in most contexts, $ r = 0 $ is not allowed because it makes the sequence collapse.
- But look at the options: c. 0
- Actually, r = 0 is not acceptable because:
- $ a_2 = a_1 \cdot r = 0 $
- $ a_3 = a_2 \cdot r = 0 \cdot 0 = 0 $
- So ratio $ \frac{a_3}{a_2} = \frac{0}{0} $ → undefined!
- So common ratio cannot be 0 because it leads to undefined ratios.
- ✔ Answer: c. 0
---
11. Which of the following is a geometric sequence?
Check each:
a. 3, 7, 11, 15 → differences: +4 → arithmetic, not geometric
b. $ \frac{1}{2}, \frac{1}{3}, \frac{2}{9}, \dots $
- Check ratios:
- $ \frac{1/3}{1/2} = \frac{2}{3} $
- $ \frac{2/9}{1/3} = \frac{2}{9} \cdot 3 = \frac{2}{3} $
- Ratio = $ \frac{2}{3} $ → constant
- ✔ Geometric!
c. 4, 4.5, 5 → differences: +0.5 → arithmetic
d. 2, 3, 5, 8 → no clear ratio or difference → neither
- ✔ Answer: b. $ \frac{1}{2}, \frac{1}{3}, \frac{2}{9}, \dots $
---
12. What is the common ratio of the sequence whose first term and third terms are 2 and 32, respectively?
- Let $ a_1 = 2 $, $ a_3 = 32 $
- In geometric sequence: $ a_3 = a_1 \cdot r^2 $
- $ 32 = 2 \cdot r^2 $
- $ r^2 = 16 $
- $ r = \pm 4 $
- ✔ Answer: b. ±4
---
13. An arithmetic sequence has a common difference while a geometric sequence has a common _________.
- Geometric sequences have a common ratio.
- ✔ Answer: c. ratio
---
14. Which of the following is an arithmetic sequence?
Check each:
a. $ \frac{1}{2}, 1, \frac{3}{2}, \dots $
- Differences: $ 1 - 0.5 = 0.5 $, $ 1.5 - 1 = 0.5 $ → constant → yes
- ✔ Arithmetic
b. 1, -1, 1, -1 → alternates → not arithmetic
c. $ \frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \dots $ → halving → geometric
d. -2, 4, -8 → ratios: $ 4 / (-2) = -2 $, $ -8 / 4 = -2 $ → geometric
- ✔ Answer: a. $ \frac{1}{2}, 1, \frac{3}{2}, \dots $
---
15. Which of these is a geometric sequence?
a. 2, 5, 8, 11 → differences: +3 → arithmetic
b. 1, 0, 0, 0 → ratios: $ 0/1 = 0 $, $ 0/0 $ → undefined → not geometric
c. -2, 4, -8 → ratio: $ 4 / (-2) = -2 $, $ -8 / 4 = -2 $ → common ratio = -2 → geometric
d. -2, -4, -6 → differences: -2 → arithmetic
- ✔ Answer: c. -2, 4, -8, ...
---
✔ Final Answers:
| Q# | Answer |
|----|--------|
| 1 | a. 12 |
| 2 | c. $ a_n = 5n + 6 $ |
| 3 | d. 41 |
| 4 | a. positive |
| 5 | d. $ a_1 + 3d $ |
| 6 | b. $ a_n = 6n $ |
| 7 | c. average |
| 8 | d. mean |
| 9 | c. any number |
|10 | c. 0 |
|11 | b. $ \frac{1}{2}, \frac{1}{3}, \frac{2}{9}, \dots $ |
|12 | b. ±4 |
|13 | c. ratio |
|14 | a. $ \frac{1}{2}, 1, \frac{3}{2}, \dots $ |
|15 | c. -2, 4, -8, ... |
Let me know if you'd like this formatted as a printable answer key!
Parent Tip: Review the logic above to help your child master the concept of arithmetic geometric sequence worksheet.
