Class 11

Math

Algebra

Sequences and Series

The sum of (x+5) observations is $(x_{4}−625)$. Find the mean of the observations.

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Show that $a_{1},a_{2},…,a_{n},…$form an AP where $a_{n}$is defined as below : (i) $a_{n}=3+4n$ (ii) $a_{n}=9−5n$. Also find the sum of the first 15 terms in each case.

A person has 2 parents, 4 grandparents, 8 great grand parents, and so on. Find the number of his ancestors during the ten generations preceding his one.

Find the sum of all two digit numbers which when divided by 4, yields 1 as remainder.

In an A.P., the first term is 2 and the sum of the first five terms is one-fourth of the next five terms. Show that 20th term is $112$.

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

A manufacturer reckons that the value of a machine, which costs him Rs. 15625, will depreciate each year by 20%. Find the estimated value at the end of 5 years.

If $a−bxa+bx =b−cxb+cx =c−dxc+dx (x=0),$then show that a, b, c and d are in G.P.

In a GP the 3rd term is 24 and the 6th term is 192. Find the 10th term.