1 If the 2nd and 5th terms of a G. P are 6 and 48 respectively, find the sum of the first for term

If the first term is , then the second term is , the third is , the fourth is , and the fifth is .

We're given

So the first five terms in the GP are

3, 6, 12, 24, 48

Adding up the first four gives a sum of 45.

If you were asked to find the sum of many, many more terms, having a formula for the n-th partial sum would convenient. Let denote the sum of the first n terms in the GP:

Multiply both sides by 2:

Subtract this from , which eliminates all the middle terms:

Then the sum of the first four terms is again .

step-by-step explanation:

for the free