Class 11

Math

Algebra

Sequences and Series

A.M. of $1,2,x,3$ is $0$, then $x=$ _____.

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If the 3rd and the $9_{th}$terms of an AP are 4 and $−8$ respectively, which term of this AP is zero?

Find the sum of all numbers between 200 and 400 which are divisible by 7.

Subba Rao started work in 1995 at an annual salary of Rs 5000 and received an increment of Rs 200 each year. In which year did his income reach Rs 7000?

If A and G be A.M. and GM., respectively between two positive numbers, prove that the numbers are $A±(A+G)(A−G) $.

Find the indicated terms of the sequence whose $n_{th}$terms are : $a_{n}=n+3n(n−2) $; $a_{20}$

Insert three numbers between 1 and 256 so that the resulting sequence is a G.P.

A sum of Rs 700 is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is Rs 20 less than its preceding prize, find the value of each of the prizes.

Write the first five terms of the sequence and obtain the corresponding series : $a_{1}=3,a_{n}=3a_{n−1}+2$for all $n>1$