The sum of infinity and the second term of a geometric progression are 4 and 1 respectively. Find the, 1 common ratio, 2 the first term.

Answer 1

S_∞ = a/(1/r) so
a/(1-r) = 4
ar = 1
divide, and you have
r(1-r) = 1/4
r^2 - r + 1/4 = 0
(r - 1/2)^2 = 0
r = 1/2
so a/2 = 1
a = 2

check: 2/(1 - 1/2) = 4