Question

Write an explicit formula for the nth term or the sequence 8,-24, 72

Answer 1

`T_n =-(8)/(3) (-3)^(n)`

Explanation:

Given

`Sequence: 8, -24, 72`

Required

Determine the n term

The above sequence is geometric. So, we calculate the common ratio first:

`r = (T_2)/(T_1)`

`r = (-24)/(8)`

`r = -3`

The equation is then calculated using:

`T_n = ar^(n-1)`

Where

`a = T_1 = 8`

and

`r = -3`

The equation becomes:

`T_n =8 * (-3)^(n-1)`

Apply law of indices:

`T_n =8 * (-3)^(n) * (-3)^(-1)`

`T_n =8 * (-3)^(n) * (1)/(-3)`

`T_n =-8 * (-3)^(n) * (1)/(3)`

`T_n =-(8)/(3) * (-3)^(n)`

`T_n =-(8)/(3) (-3)^(n)`