Sequences and Series
Between 1 and 31 we inserted m arithmetic means, so that ratio of the 7th and (m−1)th means is 5:9. Then the value of m is
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denote the rth term of a G.P. for r=1,2,3,
If for some positive integers mandn,
we have Tm=1/n2
, then find the value of Tm+n/2.
Given two A.P. 2,5,8,11……T60 and 3,5,79,………T50˙ Then find the number of terms which are identical.
In a geometric progression consisting of positive terms, each term equals the sum of the next terms. Then find the common ratio.
Find the number of terms in the series 20,1931,1832…
the sum of which is 300. Explain the answer.
are in H.P., then prove that (b+c+d)/a,(c+d+a)/b,(d+a+b)/c
, are in A.P.
If a,b,c,d are in G.P. prove that (an+bn),(bn+cn),(cn+dn) are in G.P.
The 8th and 14th term of a H.P. are 1/2 and 1/3, respectively. Find its 20th term. Also, find its general term.
Find the sum of the following series :