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

Answer:

option B

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:

$\sf a_6 = a_{6-1}-3 = -5-3 = -8$