Two infinite geometric progressions have first terms and respectively

MATHEMATICS · Subjective · CBSE · Mathematics · Sequences and Series · Sequences and Series

Problem

Two infinite geometric progressions have first terms

10

and

6

respectively. The common ratio of the first is

r

while that of the second is

\tfrac12

. The sum of the first progression exceeds the sum of the second by

8

, and the larger sum is

\tfrac53

times the smaller. Determine the value of

r