List of top Mathematics Questions on Sequences and Series asked in VITEEE

If one AM 'A' and two GM \( p \) and \( q \) are inserted between two given numbers, then find the value of \[ \frac{p^2}{q} + \frac{q^2}{p} \]

For a GP, \( a_n = 3(2^n) \), \( n \in \mathbb{N} \), Find the common ratio.

If \( a, b, c \) are in HP, then \( \frac{a}{b+c} = \frac{b}{c+a} = \frac{c}{a+b} \) will be in:

The value of
\[ \lim_{n\to\infty}\left[\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\cdots+\frac{1}{n(n+1)}\right] \] is equal to

If \(F\) is function such that \(F(0)=2,\ F(1)=3\), and
\[ F(x+2)=2F(x)-F(x+1)\ \text{for}\ x\geq 0, \] then \(F(5)\) is equal to

If \(a^x=b^y=c^z=d^u\) and \(a,b,c,d\) are in GP, then \(x,y,z,u\) are in

If \(p,q,r\) are all positive and are the \(p^{th}\), \(q^{th}\) and \(r^{th}\) terms of a geometric progression respectively, then the value of the determinant
\[ \left|\begin{matrix} \log x & p & 1 \\ \log y & q & 1 \\ \log z & r & 1 \end{matrix}\right| \] equals

Let \(\alpha,\beta\) be the roots of the equation \(x^2-ax+b=0\) and \(A_n=\alpha^n+\beta^n\). Then \(A_{n+1}-aA_n+bA_{n-1}\) is equal to

If \( H \) is the harmonic mean between \( P \) and \( Q \), then the value of \[ \frac{H}{P} + \frac{H}{Q} \] is

Everybody in a room shakes hands with everybody else. The total number of handshakes in the room is

Consider an infinite geometric series with the first term and common ratio. If its sum is 4 and the second term is \( \frac{3}{4} \), then:

Series of 6, 9_ ,12, 24