Question

⎩ ⎪ ⎪ ⎨ ⎪ ⎪ ⎧ ​ a(1)=−13 a(n)=a(n−1)+4 ​ Find the 2nd2^{\text{nd}} 2 nd 2, start superscript, start text, n, d, end text, end superscript term in the sequence

Answer 1

In the sequence a(1) = -13 and a(n) = a(n-1) + 4, the 2nd term is -9. The sequence progresses with a constant increase of 4 between terms: -13, -9, -5, -1, 3, ....

The sequence defined by
`\(a(1) = -13\)` and
`\(a(n) = a(n-1) + 4\)` forms an arithmetic progression.

To find the 2nd term a(2), we apply the recurrence relation:
`\(a(2) = a(1) + 4 = -13 + 4 = -9\)`.

This yields the second term in the sequence as -9. Each subsequent term in the sequence can be obtained by adding 4 to the previous term.

The progression unfolds as follows:
`-13, -9, -5, -1, 3, \ldots`.

The common difference between consecutive terms is 4, indicating a steady arithmetic increase.

Understanding the recurrence relation allows for the determination of specific terms and the overall behavior of the sequence.

Therefore, the 2nd term in the sequence is -9.

Answer 2

a(2) = -9

Explanation:

It looks like you want the 2nd term in the arithmetic sequence defined by the recursive formula ...

• a(1) = -13
• a(n) = a(n -1) +4

Using the formula with n=2, we have ...

a(2) = a(1) +4

a(2) = -13 +4 . . . . substitute the value of a(1)

a(2) = -9