Sequences and Series · Mathematics · BITSAT

Let $$\frac{1}{16}, a$$ and $$b$$ be in GP and $$\frac{1}{a}, \frac{1}{b}, 6$$ be in AP, where $$a, b>0$$. Then, $$72(a+b)$$ is equal to

If $$a_1, a_2, \ldots, a_n$$ are in HP, then the expression $$a_1 a_2+a_2 a_3+\ldots+a_{n-1} a_n$$ is equal to

Given, a sequence of 4 numbers, first three of which are in GP and the last three are in AP with common difference 6. If first and last term of this s...

Let a1, a2, ...... a40 be in AP and h1, h2, ..... h10 be in HP. If a1 = h1 = 2 and a10 = h10 = 3, then a4h7 is...

Let a1, a2, a3 .... be a harmonic progression with a1 = 5 and a20 = 25. The least positive integer n for which an ...

In a sequence of 21 terms, the first 11 terms are in AP with common difference 2 and the last 11 terms are in GP with common ratio 2. If the middle te...

If a + 2b + 3c = 12, (a, b, c $$\in$$R+), then the maximum value of ab2c3 is

Sum of n terms of the infinite series 1.32 + 2.52 + 3.72 + ..... $$\infty$$ is

If a1, a2, a3, ......., a20 are AM's between 13 and 67, then the maximum value of a1, a2, a3, ......, a20 is equal to...

If p, q, r are in AP and are positive, the roots of the quadratic equation px2 + qx + r = 0 are all real for

If one GM, g and two AM's p and q are inserted between two numbers a and b, then (2p $$-$$ q) (p $$-$$ 2q) is equal to

Given that x, y, and z are three consecutive positive integers and x $$-$$ z + 2 = 0, what is the value of $${1 \over 2}{\log _e}x + {1 \over 2}{\log ...

The value of the sum $$\sum\limits_{k = 1}^\infty {\sum\limits_{n = 1}^\infty {{k \over {{2^{n + k}}}}} } $$ is