Question

An arithmetic sequence is represented by the recursive formula a1=17an=an−1−8 . What is the fourth term in the sequence? a4=−4 a4=−7 a4=−9 a4=−14

Answer 1

a₄ = - 15

Explanation:

Using the recursive formula and a₁ = 17 , then

a₂ = a₁ - 8 = 17 - 8 = 9

a₃ = a₂ - 8 = 9 - 8 = 1

a₃ = a₂ - 8 = 1 - 8 = - 7

a₄ = a₃ - 8 = - 7 - 8 = - 15

Answer 2

The correct option is b.

The fourth term in the sequence is
`\(a_4 = -7\)`.

To find the fourth term in the arithmetic sequence represented by the recursive formula
`\(a_1 = 17\)` and
`\(a_n = a_(n-1) - 8\)`, we can use the recursive formula to generate the terms one by one. Here's a step-by-step process:

1. Start with the given value of
`\(a_1 = 17\)`.

2. Use the recursive formula to find
`\(a_2\)`:

`\[a_2 = a_1 - 8 = 17 - 8 = 9\]`

3. Use the recursive formula again to find
`\(a_3\)`:

`\[a_3 = a_2 - 8 = 9 - 8 = 1\]`

4. Finally, use the recursive formula one more time to find
`\(a_4\)`:

`\[a_4 = a_3 - 8 = 1 - 8 = -7\]`

So, the fourth term in the sequence is
`\(a_4 = -7\)`.

Therefore, the answer is:
`\(a_4 = -7\)`.