Question

What is the sum of the first eight terms of a geometric series who’s first term is 3 and who’s common ratio is 1/2?

Answer 1

The sum of 8 terms = 5.98

Explanation:

Formula:-

Sum of n terms of GP = a(1-rⁿ)/(1-r)

a - first term

r common ratio

It is given that,

In a GP first term is 3 and who’s common ratio is 1/2

To find the sum of 8 terms

Sum of n terms of GP = a(1-rⁿ)/(1-r)

a = 3 , r = 1/2 and n = 8

sum = 3(1 - (1/2)⁸)/(1 - 1/2)

= 3(1 - (1/2)⁸)/(1/2)

= 6(1 - 0.0039) = 5.98

Therefore sum of 8 terms = 5.98

Answer 2

Answer: 765/128 or 5.97

Explanation:

You know that:

- The first term of the geometric serie is 3.

- The common ratio is 1/2 (r=1/2).

Therefore, you can apply the following formula:

`Sn=(a_1(1-r^(n)))/(1-r)`

Where
`a_1` is the first term, n i the number of terms and r is the common ratioo.

Substitute values and you obtain:

`Sn=(3(1-(1/2)^(8)))/(1-(1/2))=765/128=5.97`