(a) Prove that if k real numbers are inserted between two unequal positive numbers a…
MATHEMATICS · Subjective · CBSE · Mathematics · Sequences and Series · Sequences and Series
Problem
(a) Prove that if k real numbers are inserted between two unequal positive numbers a and b so that all the numbers form a geometric progression, then the common ratio r satisfies rk+1=ab.
(b) Using part (a), insert four numbers between 27 and 271 so that the entire sequence is a geometric progression.
(c) Find the sum of all six terms of the progression obtained in part (b).