Question

The first term in a geometric series is 64 and the common ratio is 0. 75.

Find the sum of the first 4 terms in the series

Answer 1

Explanation:

The geometric sum formula for finite terms is given as:

If r = 1, Sn = na

If |r| < 1 ,

Sn = a(1 − r^n)/(1 − r)

If |r| > 1,

Sn = a(r^n − 1)/(r - 1)

in our case

a = s1 = 64

r = 0.75, which is smaller than 1.

so, we get

S4 = 64(1 - 0.75⁴)/(1 - 0.75) =

= 64(1 - 0.31640625)/0.25 =

= 64×0.68359375/0.25 = 175

quick check :

s1 = 64

s2 = s1×0.75 = 64×0.75 = 48

s3 = s2×0.75 = 48×0.75 = 36

s4 = s3×0.75 = 36×0.75 = 27

and the sum of these 4 items is : 175

all is correct !

Answer 2

The answer is down below