Question

given a geometric progression of 5.10,20 ... find the sum of all terms from the fifth term to the ninth term

Answer 1

You could find S(9) - S(4)
a = 5 and r = 2
S(9) = 5(2^9 - 1)/(2 - 1) = 2555
S(4) = 5(2^4 - 1)/(2 - 1) = 75
The terms from 5th to 9th add to 2555 - 75 = 2480

The other alternative method is the find the 5th term and add 5 terms starting from there
T(5) = 5 x 2^(5 - 1) = 80
New sequence has a = 80 and r = 2
S(5) = 80(2^5 - 1)/(2 - 1) = 80 x 31 = 2480