Sequences and Series
The AM between two positive numbers a and b(a>b) is twice their GM. Prove that a:b=(2+3):(2−3).
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Let x=1+a+a2+…and y=1+b+b2+…, where ∣a∣<1and ∣b∣<1. Prove that 1+ab+a2b2+…=x+y−1xy
Find the sum of the products of the corresponding terms of the sequences 2,4, 8, 16, 32 and 128, 32, 8, 2, 21.
The difference between any two consecutive interior angles of a polygon is 5o. If the smallest angle is 120o, find the number of the sides of the polygon.
If A.M. and GM. of roots of a quadratic equation are 8 and 5, respectively, then obtain the quadratic equation.
How many terms of G.P. 3,32,33,˙˙˙are needed to give the sum 120?
Find the sum of all numbers between 200 and 400 which are divisible by 7.
Find the sum of all two digit numbers which when divided by 4, yields 1 as remainder.
Find the sum of the following APs : (i) 2, 7, 12, . . . , to 10 terms.