Question

Given the following sequence, find the 12th term: {2, -4, 8,...} -4096 4096 2048 -2048

Answer 1

Answer:

- 4096

Step-by-step explanation:

There is a common ratio between consecutive terms of the sequence.

r = - 4 ÷ 2 = 8 ÷ - 4 = - 2

This indicates 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 = 2 and r = - 2 , thus

$a_{12}$ = 2 × $(-2)^{11}$ = 2 × - 2048 = - 4096