Question

Find a formula for the general term an of the sequence, assuming that the pattern of the first few terms continues. (Assume that n begins with 1.) {-4, 8/3, -16/9, 32/27, -64/81, . . . } an =

Answer 1

Step-by-step explanation:

a1 = -4 = -4/1, a2 = 8/3

r = a2/a1 = (8/3) / (-4/1) = -2/3

the formula :

an = a1. r^(n-1)

so,

an = (-4). (-2/3)^(n-1)

Answer 2

Step-by-step explanation:

$-4, \dfrac{8}{3}, -\dfrac{16}{9}, \dfrac{32}{27}, -\dfrac{64}{81},..., (-1)^n\dfrac{2^{n + 1}}{3^{n - 1}}, ...$