class 11

Math

Algebra

Sequences and Series

If x, y, z are in A.P. and $tan_{−1}x,tan_{−1}yandtan_{−1}z$are also in A.P., then

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If the sum of the first 14 terms of an AP is 1050 and its first term is 10, find the $20_{th}$ term.

Let the sum of n, 2n, 3n terms of an A.P. be $S_{1},S_{2}$and $S_{3}$, respectively, show that $S_{3}=3(S_{2}−S_{1})$.

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.

If $a_{n−1}+b_{n−1}a_{n}+b_{n} $is the A.M. between a and b, then find the value of n.

Which term of the AP : 121, 117, 113, . . ., is its first negative term?[Hint : Find n for $a_{n}<0$]

If the sum of three numbers in A.P., is 24 and their product is 440, find the numbers.

In an A.P., if $p_{th}$term is $q1 $and $q_{th}$term is $p1 $, prove that the sum of first pq terms is $21 (pq+1),$where $p=q$.

Find the sum to indicated number of terms in each of the geometric progressions : $x_{3},x_{5},x_{7},n˙˙˙$terms $(ifx=±1)$.