Class 11

Math

Algebra

Sequences and Series

A.M. of $a−2$, $a$, $a+2$ is ____.

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The sum of three numbers in GP. Is 56. If we subtract 1, 7, 21 from these numbers in that order, we obtain an arithmetic progression. Find the numbers.

Write the first three terms of the sequence defined by $a_{1}=2,a_{n+1}=a_{n}+22a_{n}+3 $ .

Divide 32 into four parts which are in A.P. such that the ratio of the product of extremes to the product of means is 7:15.

The harmonic mean between two numbers is 21/5, their A.M. $_{′}A_{′}$ and G.M. $_{′}G_{′}$ satisfy the relation $3A+G_{2}=36.$ Then find the sum of square of numbers.

Find the sum of $n$ terms of the series $1+54 +5_{2}7 +5_{3}10 +˙$

Find the sum to $n$ terms of the series $1+1_{2}+1_{4}1 +1+2_{2}+2_{4}2 +1+3_{2}+3_{4}3 +……….$ that means $t_{r}=r_{4}+r_{2}+1r $ find $1∑n $

If $a,b,andc$ be in G.P. and $a+x,b+x,andc+x$ in H.P. then find the value of $x(a,bandcaredist∈ctνmbers)$ .

If $p,q,andr$ are inA.P., show that the pth, qth, and rth terms of any G.P. are in G.P.