Sequences and Series
The minimum value of the sum of real numbers a−5, a−4,3a−3,1, a8 and a10 with a>0 is
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The sum of some terms of G. P. is 315 whose first term and the common ratio are 5 and 2, respectively. Find the last term and the number of terms.
If an−1+bn−1an+bnis the A.M. between a and b, then find the value of n.
For what value of n, are the with terms of two APs: 63, 65, 67, . . . and 3, 10, 17, . . . equal?
Find the sum of the following series up to n terms : 113+1+313+22+1+3+513+23+33+˙˙˙
The first term of an AP is 5, the last term is 45 and the sum is 400. Find the number of terms and the common difference.
If the sum of the first 14 terms of an AP is 1050 and its first term is 10, find the 20th term.
Find the indicated terms of the sequence whose nthterms are : an=4n−3;a17,a24
If the 4th, 10thand 16thterms of a G.P. are x, y and z, respectively. Prove that x, y, z are in G.P.