Sequences and S...

In a GP of positive terms, if every term is equal to the sum of the next two terms. Find the common ratio of the GP.

The harmonic mean of two numbers is 4, Their arithmetic mean A and the geometric mean G satisfy the relation 2A + G² = 27, then the two numbers are:

Find the sum of the sequence -8, -5, -2, …, 7.

The first term of a GP is 1. The sum of the third term and fifth term is 90. The common ratio of GP is:

The sum of the series 5 + 9 + 13 + … + 49 is:

Find the sum of the series 5 + 55 + 555 + ..... upto n terms.

What is the sum of first eight terms of the series \(1-\frac{1}{2}+\frac{1}{4}-\frac{1}{8}+\ldots ?\)

If the sequence \(\left\{ S _{ n }\right\}\) is a geometric progression and \(S _{2} S _{11}= S _{ p } S _{8}\), then what is the value of \(p\)?

If the GM and AM between two number are in the ratio n : m, then what is the ratio between the two numbers?

If \(\frac{a^{n+1}+b^{n+1}}{a^{n}+b^{n}}\) be the harmonic mean of \(a\) and \(b\) then value of \(n\) is: