Question

the common ratio of a geometric series is 3 and the sum of the first 8 terms is 3280. what is the first term of the series?

Answer 1

1

Explanation:

Answer 2

Answer: 1

Explanation:

The formula for calculating the sum of a Geometric series if the common ratio is greater than 1 is given as :

`S_(n)` =
`(a(r^(n)-1) )/(r-1)`

Where
`S_(n)` is the sum of terms , a is the first term , r is the common ratio and n is the number of terms.

From the question:

`S_(n)` = 3280

a = ?

r = 3

n = 8

Substituting this into the formula , we have

3280 =
`(a(3^(8)-1) )/(3-1)`

3280 =
`(a(6561-1))/(2)`

Multiply through by 2 , we have

6560 = a ( 6560)

divide through by 6560, we have

6560/6560 = a(6560)/6560

Therefore : a = 1

The first term of the series is thus 1