Sequences and Series
If the sum of n terms of an A.P. is 3n2+5n and its mth term is 164, find the value of m.
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The sum of the 4th and 8th terms of an AP is 24 and the sum of the 6th and 10th terms is 44. Find the first three terms of the AP.
In a flower bed, there are 23 rose plants in the first row, 21 in the second, 19 in the third, and so on. There are 5 rose plants in the last row. How many rows are there in the flower bed?
Find the sum to n terms of the series :3×a2+5×22+7×32+˙˙˙
Write the first five terms of the sequence whose nthterms are : an=n(n+2)
If f is a function satisfying f(x+y)=f(x)f(y)for all x,y∈Xsuch that f(1)=3and x=1∑nf(x)=120, find the value of n.
The first term of a G.P. is 1. The sum of the third term and fifth term is 90. Find the common ratio of G.P.
Insert 6 numbers between 3 and 24 such that the resulting sequence is an A. P.
If the sum of n terms of an A.P. is nP+21n(n−1)Q,where P and Q are constants, find the common difference.