Question

Given a2 = 6 and a5 = –384 of a geometric sequence, what is the recursive equation for the nth term?

an = –4(an – 1), a1 = –1.5
an = –4(an – 1), a1 = 1.5
an = 4(an – 1), a1 = –1.5
an = 4(an – 1), a1 = 1.5

Answer 1

Please see the image that I've included. The answer is option A.

Answer 2

`a_n = (-4)^(n - 1); a_1 = -1.5`

Explanation:

`a_1 = a_1`

`a_2 = a_1 * r`

`a_3 = a_1 * r^2`

`a_4 = a_1 * r^3`

`a_5 = a_1 * r^4`

`a_1 * r = 6`

`a_1 * r^4 = -384`

`r = (6)/(a_1)`

`a_1 * ((6)/(a_1))^4 = -384`

`r = (6)/(a_1)`

`(1296)/(a_1)^3} = -384`

`r = (6)/(a_1)`

`(1)/(a_1)^3} = -(384)/(1296)`

`r = (6)/(a_1)`

`a_1^3 = -(27)/(8)`

`r = (6)/(a_1)`

`a_1 = -1.5`

`r = (6)/(-1.5)`

`a_1 = -1.5`

`r = -4`

`a_1 = -1.5`

`a_n = (-4)^(n - 1); a_1 = -1.5`