Sequences and Series
The AM between two positive numbers a and b(a>b) is twice their GM. Prove that a:b=(2+3):(2−3).
A G.P. consists of an even number of terms. If the sum of all the terms is 5 times the sum of terms occupying odd places, then find its common ratio.
Between 1 and 31, m numbers have been inserted in such a way that the resulting sequence is an A. P. and the ratio of 7thand (m−1)thnumbers is 5 : 9. Find the value of m.