Question

What is the value of the fourth term in a geometric sequence for which a1=10 and r=0.5

Answer 1

a2 = a1 * r
a2 = 10 * .5 = 5
a3 = a2 * r
a3 = 5 * .5 = 2.5
a4 = a3 * r
a4 = 2.5 * .5 = 1.25

the answer is 1.25

Answer 2

Find out the the value of the fourth term in a geometric sequence for which

`a_(1) = 10\ and\ r =0.5`

To proof

The formula for the general term for each geometric sequence is

`a_(n) = a_(1) r^(n-1)`

where

`a_(1) = first\ term,\ r = common\ ratio`

Put n= 4

`a_(4) = 10*(0.5)^(4-1)`

`a_(4) = 10*(0.5)^(3)`

`a_(4) = 10*0.125`

Solving

`a_(4) = 1.25`

The value of the fourth term in a geometric sequence is 1.25 .

Hence proved