Question

The sum of an infinite geometric series is 450, while the common ratio of the series is 4/ 5 . What is the first term of the series? A) 22 1 2 B) 45 C) 90 D) 180

Answer 1

C) 90

Explanation:

The sum of an infinite geometric series is:

S = a₁ / (1 − r)

where a₁ is the first term and r is the common ratio.

450 = a₁ / (1 − 4/5)

450 = a₁ / (1/5)

450 = 5a₁

a₁ = 90

Answer 2

answer is 90 for first term

Explanation:

Let the terms be

First term x

We will use the formula s∞=x/1−r to find the sum of an infinite geometric series, where −1<r<1.

We know the sum and the common ratio, so we'll be solving for x where r =4/5

s∞=x/1−r

450=x/1−4/5

450=x/1/5

450=5x

x=90

this is the first term x1 = 90

we know that common ratio is 4/5, so multiplying the first term by factor 4/5 to get the second term

90 x 4/5= 72 second term