List of top Mathematics Questions on sequences asked in MET

If \(a^2, b^2, c^2\) are in A.P., then \(b+c, c+a, a+b\) are in:

If \(\log_3 2\), \(\log_3(2x-5)\) and \(\log_3(2x-\tfrac{7}{2})\) are in AP, then the value of \(x\) is

The sum of the first n terms of two AP's are in the ratio \((2n+3):(3n-1)\). The ratio of their 5th terms is

The sum of the even multiples of 9 between 300 and 500 is

If for all \(x,y \in \mathbb{N}\), there exists a function \(f(x)\) satisfying \(f(x+y)=f(x)f(y)\) such that \(f(1)=3\) and \(\sum_{x=1}^{n} f(x)=120\), then value of \(n\) is:

In \(\triangle ABC\), if \(\cot A, \cot B\) and \(\cot C\) are in AP, then \(a^2, b^2\) and \(c^2\) are in

The sum of infinite terms of the GP $\dfrac{\sqrt{2}+1}{\sqrt{2}-1},\;\dfrac{1}{2-\sqrt{2}},\;\dfrac{1}{2},\;\ldots$ is

The value of $\displaystyle\sum_{r=1}^{\infty}\left[3\cdot 2^{-r} - 2\cdot 3^{1-r}\right]$ is

The sum to $n$ terms of the series $\dfrac{1}{2} + \dfrac{3}{4} + \dfrac{7}{8} + \dfrac{15}{16} + \cdots$ is}

Let $U_{n} = 2 + 2^{3} + 2^{5} + \cdots + 2^{2n+1}$ and $V_{n} = 1 + 4 + 4^{2} + \cdots + 4^{n-1}$. Then $\displaystyle\lim_{n \to \infty} \dfrac{U_n}{V_n}$ is equal to

$\frac{1}{\log_{10} 25} + \frac{1}{\log_{10} 4} + \frac{1}{\log_{10} 10} + \frac{1}{\log_{10} 2} + \frac{1}{\log_{10} 5}$ is equal to

$0.2 + 0.22 + 0.222 + \ldots$ to n terms is equal to

If the nth term of the geometric progression, $5, -\frac{5}{2}, \frac{5}{4}, -\frac{5}{8}, \ldots$ is $\frac{5}{1024}$, then the value of n is

If $\log_3 2$, $\log_3 (2^x - 5)$ and $\log_3 \left(2^x - \frac{7}{2}\right)$ are in AP, the value of $x$ is

$\sum_{n=1}^{\infty} \frac{(-1)^{n-1}}{n(n+1)}$ is equal to

The coefficient of $x$ in the expansion of $(1+x+x^2+x^3)^{-1}$ is

The numbers $aₙ$ are defined by $a₀=1$ and $aₙ+1=3n²+n+aₙ$ for $n ≥ 0$. Then, $aₙ$ is equal to ________.

The value of \( \sum_{k=1}^{n} \frac{1}{\sqrt{a_{k}} + \sqrt{a_{k+1}}} \), where \( a_{1}, a_{2}, \dots, a_{n} \) are in A.P. with common difference \( d \), is:

If the sum of \( n \) terms of two A.P.s are in the ratio \( (3n + 8) : (7n + 15) \), then the ratio of their \( 12^{\text{th}} \) terms is:

If \( \log_{10} 2,\ \log_{10}(2^{x} - 1),\ \log_{10}(2^{x} + 3) \) are in A.P., then \( x \) is: