Question

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

Answer 1

We are told that
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

Answer 2

Is it correct

Answer 3

The answer is not correct the final answer is 72/25

Answer 4

The answer is very wrong the correct answer is either 72/25 or 2 22/25

Answer 5

We are told that
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)
=8/5 + 32/25

Answer 6

Final answer =72/25