Question

Write a recursive formula for the sequence 7, 4, 1, -2, -5, .... Then find the next term.

A.
`a_(n) = a_(n - 1) - 3`, where
`a_(1) = -8`; 7

B.
`a_(n) = a_(n - 1) - 3`, where
`a_(1) = 7`; -8

C.
`a_(n) = a_(n - 1) + 3`, where
`a_(1) = -3`; 22

D.
`a_(n) = a_(n - 1) + 3`, where
`a_(1) = 7`; -8

Answer 1

option B

Step-by-step explanation:

Recursive Formula: aₙ = aₙ₋₁ + d

Given Sequence: 7, 4, 1, -2, -5,....

Identify the common difference:

second term - first term

4 - 7 = -3 or 1 - 4 = -3 or -2 - 1 = -3

So formula:

`\sf a_n = a_(n-1)-3`, where
`\sf a_1 = 7`

Find next term:

`\sf a_6 = a_(6-1)-3 = -5-3 = -8`