Question

An arithmetic sequence has this recursive formula: (a^1 =8, a^n= a^n-1 -6

A.a^n=8+(n-6)(-1)
B.a^n=8+(n-1)(-6)
C.

Answer 1

`a_n = 8 + (n - 1) (-6)`

Explanation:

Given

`a_1 = 8`

Recursive:
`a_(n) = a_(n-1) - 6`

Required

Determine the formula

Substitute 2 for n to determine
`a_2`

`a_(2) = a_(2-1) - 6`

`a_(2) = a_(1) - 6`

Substitute
`a_1 = 8`

`a_2 = 8 - 6`

`a_2 = 2`

Next is to determine the common difference, d;

`d = a_2 - a_1`

`d = 2 - 8`

`d = -6`

The nth term of an arithmetic sequence is calculated as

`a_n = a_1 + (n - 1)d`

Substitute
`a_1 = 8` and
`d = -6`

`a_n = a_1 + (n - 1)d`

`a_n = 8 + (n - 1) (-6)`

Hence, the nth term of the sequence can be calculated using
`a_n = 8 + (n - 1) (-6)`