Question

Find an explicit rule for the nth term of the sequence.

-2, -8, -32, -128

Answer 1

Answer:

$a_{n}$ = - 2 $(4)^{n-1}$

Step-by-step explanation:

There is a common ratio between consecutive terms , that is

r = - 8 ÷ - 2 = - 32 ÷ - 8 = - 128 ÷ - 32 = 4

This indicates the sequence is geometric with nth term

$a_{n}$ = a₁ $(r)^{n-1}$

where a₁ is the first term and r the common ratio

Here a₁ = - 2 and r = 4 , then explicit formula is

$a_{n}$ = - 2 $(4)^{n-1}$