Question

What is the 16th term in the following geometric sequence?
5, −10, 20, −40, 80,...

Answer 1

Answer: -163840

Step-by-Step Explanation:

As we can see, starting from the first term, every term is repeatedly multiplied by (-2) in order to form this sequence.

1) 5
2) 5 * -2 = -10
3) -10 * -2 = 20
4) 20 * -2 = -40
5) -40 * -2 = 80
6) 80 * -2 = -160
7) -160 * -2 = 320
8) 320 * -2 = -640
9) -640 * -2 = 1280
10) 1280 * -2 = -2560
11) -2560 * -2 = 5120
12) 5120 * -2 = -10240
13) -10240 * -2 = 20480
14) 20480 * -2 = -40960
15) -40960 * -2 = 81920
16) 81920 * -2 = -163840
17) -163840 * -2 =327680

Therefore, 16th Term = -163840

Answer 2

-163840

Step-by-step explanation:

The formula to find the nth term for a geometric sequence is

(a1)(r)^n-1

So by plugging in the terms you get

(5)(-2)^16-1 = -163840