Theory question 101
Sequences and SeriesThe second term of a geometric progression is 3. If its sum to infinity is 25/2, find the value of the common ratio.
Show the model answer
Model answer
ar = 3 and a/(1 − r) = 25/2
a = 3/r, so 3/(r(1 − r)) = 25/2
25r − 25r² = 6, 25r² − 25r + 6 = 0
(5r − 3)(5r − 2) = 0
r = 3/5 or r = 2/5 (both have |r| < 1, so both are valid)
Explanation
Eliminate a between the two equations to get a quadratic in r.