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