Use the formula for the sum of the first n terms of a geomet

Use the formula for the sum of the first n terms of a geometric sequence to find the sum of the first five terms of the geometric sequence 3/2, 3/8, 3/32.. ..

Solution

sum of n terms of geometric sequence is given by ,s_n=a(rⁿ-1)/(r-1)

a is the first term and r is the common ratio

3/2, 3/8,3/32,......

the common ratio is 3/8/3/2=1/4

and a=3/2

therefore

s₅= 3/2(1/4^5-1)/(1/4-1)

s₅= 1023/512