Let `{a _(1),a _(2), a _(3)......}` be a strictly increasing sequence of positive integers in an arithmetic progression. Prove that there is an infinite subsequence of the given sequence whose terms are in a geometric progression.

Determine the arithmetic progression whose 3rd term is 5 and 7th term is 9.

solve x^3-7x^2+14x-8=0 given that the roots are in geometric progression.

The least positive term of an arithmetic progression whose first two term are (5)/(2) and (23)/(12) is

The first three terms of a geometric progression are 48,24,12 . What are the common ratio and fourth term of this sequence ?

Find the indicated terms in each of the following arithmetic progression 5,2,-1…..t_10

If p^("th"), 2p^("th") and 4p^("th") terms of an arithmetic progression are in geometric progression, then the common ratio of the geometric progression is

Find three numbers a, b, c between 2 and 18 such that: (i) their sum is 25, and (ii) the numbers 2, a, b are consecutive terms of an arithmetic progression, and (iii) the numbers b, c, 18 are consecutive terms of a geometric progression.

Find the sum of the following arithmetic progression: 3,9/2,6,15/2,……….. to 25 terms.