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

Answer: 1

Step-by-step explanation:

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

$S_{n}$ = $\frac{a(r^{n}-1) }{r-1}$

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 = $\frac{a(3^{8}-1) }{3-1}$

3280 = $\frac{a(6561-1)}{2}$

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