Word Problems For Geometric Sequence - Free Printable

Let's solve this step by step based on the information provided in the image.

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Problem Summary:

Sally grows strawberries:
- Year 1: 6 seeds
- Year 2: 18 seeds
- Year 3: 54 seeds

We are given a table:

| X (Year) | 1 | 2 | 3 |
|----------|---|---|---|
| Y (Seeds)| 6 | 18| 54|

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Part A: Is this arithmetic or geometric?

#### Step 1: Check if it’s arithmetic
In an arithmetic sequence, the difference between consecutive terms is constant.

Check the differences:
- 18 - 6 = 12
- 54 - 18 = 36

The differences are not constant (12 ≠ 36), so it's not arithmetic.

#### Step 2: Check if it’s geometric
In a geometric sequence, the ratio between consecutive terms is constant.

Check the ratios:
- 18 / 6 = 3
- 54 / 18 = 3

The ratio is constant (3), so this is a geometric sequence.

✔ Answer to A: This is a geometric sequence.

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Part B: How many seeds will she plant in her 8th year?

We have a geometric sequence where:
- First term $ a = 6 $
- Common ratio $ r = 3 $
- We want the 8th term: $ a_8 $

The formula for the $ n $th term of a geometric sequence is:

$$
a_n = a \cdot r^{n-1}
$$

Plug in the values:

$$
a_8 = 6 \cdot 3^{8-1} = 6 \cdot 3^7
$$

Now calculate $ 3^7 $:

- $ 3^1 = 3 $
- $ 3^2 = 9 $
- $ 3^3 = 27 $
- $ 3^4 = 81 $
- $ 3^5 = 243 $
- $ 3^6 = 729 $
- $ 3^7 = 2187 $

Now multiply:

$$
a_8 = 6 \cdot 2187 = 13,122
$$

✔ Answer to B: She will plant 13,122 seeds in her 8th year.

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✔ Final Answers:

A) This is a geometric sequence.
B) She will plant 13,122 seeds in her 8th year.