Question

What is the fifth term of the sequence whose first term is 10 and whose common ratio is 1/2?
A.160
B.50
C.12
D.5/8

Answer 1

nth term of an arithmetic sequence is given as
\[a_n=a_1r^{(n-1)}\]
a_1= first term
r= common ratio
a_n= nth term
here n=5 \(a_1=10\) and common ratio \(=\frac{1}{2}\), can you find the fifth term now?

Answer 2

Think of it like this.

First term - 10
Second - 10 * 1/2
Third - (10 * 1/2) * 1/2
Fourth - (10 * 1/2 * 1/2) * 1/2
Fifth - (10 * 1/2 * 1/2 * 1/2) * 1/2

Answer 3

So first find 1/2 * 1/2 * 1/2 * 1/2.

\( \color{Black}{\Rightarrow ({1 \over 2})^4 = {1 \over 2^4} = {1 \over 16}}\)

Now find 10 * 1/16

Answer 4

is it 5/8?

Answer 5

Yep