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

Answer

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

$a_{4} = 10\times(0.5)^{4-1}$

$a_{4} = 10\times(0.5)^{3}$

$a_{4} = 10\times0.125$

Solving

$a_{4} = 1.25$

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

Hence proved