Let's solve each of the three problems step by step.
---
Problem 1:
If the sum of four consecutive integers is 26, what is the value of the first integer?
#### Step-by-step:
Let the four consecutive integers be:
- $ x $
- $ x + 1 $
- $ x + 2 $
- $ x + 3 $
Their sum is:
$$
x + (x+1) + (x+2) + (x+3) = 4x + 6
$$
We are told this sum equals 26:
$$
4x + 6 = 26
$$
Subtract 6 from both sides:
$$
4x = 20
$$
Divide by 4:
$$
x = 5
$$
✔ So, the first integer is
5.
>
✔ Answer: 5
---
Problem 2:
If there are five even consecutive integers in a series and the first integer is 0, what is the value of the last consecutive integer?
Even consecutive integers increase by 2 each time.
Starting at 0:
- 1st: 0
- 2nd: 2
- 3rd: 4
- 4th: 6
- 5th: 8
So the last (fifth) integer is
8.
✔ Answer: 8
---
Problem 3:
In a series of five ascending odd consecutive integers, with 31 being the first integer, what is the sum of the five integers?
Odd consecutive integers increase by 2.
Given first integer = 31
So the five integers are:
- 31
- 33
- 35
- 37
- 39
Now add them:
$$
31 + 33 = 64 \\
64 + 35 = 99 \\
99 + 37 = 136 \\
136 + 39 = 175
$$
Alternatively, use the formula for the sum of an arithmetic sequence:
$$
\text{Sum} = \frac{n}{2} \times (\text{first} + \text{last}) = \frac{5}{2} \times (31 + 39) = \frac{5}{2} \times 70 = 5 \times 35 = 175
$$
✔ Answer: 175
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✔ Final Answers:
1.
5
2.
8
3.
175
These match the options provided.
Parent Tip: Review the logic above to help your child master the concept of consecutive integers word problems worksheet.
