Question

for the geometric progression 20,5,1and half. find (1)the common ratio (2)the n the term (3)the sum of the first 8 term

Answer 1

You claim it is a GP, so the common ratio must be 5/20 = 1/4
so the 3rd term should be 5/4, which is not what you stated.

term(n) = ar^(n-1) = 20(1/4)^(n-1)
= (5)(4)(1/4)^(n-1)
= 5(4)(4)^(1-n)
= 5(4)^(2-n)

sum(8) = a(1 - r^8)/(1 - r)
= 20(1 - (1/4)^8)/(3/4)
= (80/3)(1 - 1/65536)
= (80/3)(65535/65536)
= 109225/4096 or appr 26.667

Answer 2

Please help me find the 7th term