Question

The first term of a gp is twice its common ratio find the sum of the first two terms of the progression if the sum of infinity is 8

Answer 1

The first term of a gp is twice its common ratio find the sum of the first two terms of the progression if the sum of infinity is 8

a = 2r

sum of all terms = a/(1-r)
2r/(1-r) = 8
2r = 8 - 8r
10r = 8
r = 4/5
then a = 8/5
sum of first two terms = a + ar
= 8/5 + (8/5)(4/5) = 50/5 = 10

check for sum of all terms to be 8
sum(all terms) = (8/5) / (1 - 4/5)
= (8/5) / 1/5)
= 8