Class 11

Math

Algebra

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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Let $T_{r}$ denote the rth term of a G.P. for $r=1,2,3,$ If for some positive integers $mandn,$ we have $T_{m}=1/n_{2}$ and $T_{n}=1/m_{2}$ , then find the value of $T_{m+n/2.}$

Given two A.P. $2,5,8,11……T_{60}$ and $3,5,79,………T_{50}˙$ 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.

If $a,b,candd$ are in H.P., then prove that $(b+c+d)/a,(c+d+a)/b,(d+a+b)/c$ and $(a+b+c)/d$ , are in A.P.

If $a,b,c,d$ are in G.P. prove that $(a_{n}+b_{n}),(b_{n}+c_{n}),(c_{n}+d_{n})$ 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 : $0.7+0.77+0.777+→n$ terms