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

Question

Jon Cline

Mathematics

30 May, 17:13

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

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Answers (2)

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Monserrat Johnson · Answer 1

answer is 90 for first term

Step-by-step 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
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

Cason Chavez · Answer 2

C) 90

Step-by-step 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