The 3rd term of Geometric progression is 63 and 5th term 567. Find the sum of 1st 6 term

The sum of 1st to 6th term is - 1274 or 2548

Step-by-step explanation:

The general form of geometric progression is a, a*r, a*r*r, a*r*r*r, ... and so on, where a is first term, r is called common ratio, a*r is second term, a*r*r is third term, ... and so on.

If you know 3rd term and 5th term, than you can calculate a and r.

a * r * r = 63

a * r * r * r * r = 567

63 * r * r = 567

r * r = 567 / 63 = 9

r = 3 or r = - 3

a = 63 / (r * r) = 63 / 9 = 7

There are two possible sequences: (1) a=7, r=-3 or (2) a=7, r=3

The formula for calculation the sum of 1st to 6th term is a * (1 - r^6) / (1 - r)

(1) sum = 7 * (1 - 729) / 4 = 7 * (-182) = - 1274

(2) sum = 7 * (1 - 729) / (-2) = 2548