Class 11

Math

Algebra

Sequences and Series

the mean $xˉ$

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Find the sum of all natural numbers lying between 100 and 1000, which are multiples of 5.

Find the sum to infinity of the following Geometric Progression:$6,1.2,0.24,…$

Find the sum of integers from 1 to 100 that are divisible by 2 or 5.

Find a G.P. for which sum of the first two terms is $−4$and the fifth term is 4 times the third term.

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

If $S_{1},S_{2},S_{3}$are the sum of first n natural numbers, their squares and their cubes, respectively, show that $9S_{2}=S_{3}(1+8S_{1})$.

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 $p=q$.

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.