Question

Find the first five terms and the 8th term of the given geometric sequence:

an = 5(2)n-1
A) First five terms: 5, 10, 20, 40, 80; 8th term: 320
B) First five terms: 5, 10, 15, 20, 25; 8th term: 32
C) First five terms: 1, 2, 4, 8, 16; 8th term: 128
D) First five terms: 5, 15, 25, 35, 45; 8th term: 55

Answer 1

Calculating the terms of the geometric sequence given by an = 5(2)n-1, the first five terms are 5, 10, 20, 40, 80 and the 8th term is 640, indicating that all options provided are incorrect.

Step-by-step explanation:

To find the first five terms and the 8th term of the geometric sequence an = 5(2)n-1, we plug in the values of n to the formula for the terms we need.

First term (a1): for n=1
a1 = 5(2)1-1 = 5(2)0 = 5

Second term (a2): for n=2
a2 = 5(2)2-1 = 5(2)1 = 10

Third term (a3): for n=3
a3 = 5(2)3-1 = 5(2)2 = 20

Fourth term (a4): for n=4
a4 = 5(2)4-1 = 5(2)3 = 40

Fifth term (a5): for n=5
a5 = 5(2)5-1 = 5(2)4 = 80

Eighth term (a8): for n=8
a8 = 5(2)8-1 = 5(2)7 = 640

Thus, the first five terms are 5, 10, 20, 40, 80, and the 8th term is 640, not 320 as option A suggests. Therefore, all options are incorrect.