Question

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

-4, -8, -16, -32, ...

an = -4 • 2n - 1
an = 2 • -4n + 1
an = 2 • -4n
an = -4 • 2n

Answer 1

Answer:

$a_{n}$ = - 4 × $2^{n-1}$

Step-by-step explanation:

Note there is a common ratio between consecutive terms in the sequence.

r = - 8 ÷ - 4 = - 16 ÷ - 8 = - 32 ÷ - 16 = 2

This indicates that the sequence is geometric with n th term

$a_{n}$ = a $(r)^{n-1}$

where a is the first term and r the common ratio

Here a = - 4 and r = 2, thus

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