Sequence of series practice · Easy

An A.P. consists of $2 n$ terms. If two middle terms are $\alpha-\beta$ and $\alpha+\beta$, then sum of the $2 n$ terms of the A.P. is

Let $S_n$ denote the sum of the first $n$ terms of an A.P. $a_1, a_2, a_3, \ldots, a_n$. If $a_5+a_9=1$ and $S_9=6$, then which of the following is not true?

The value of $2.\overline {357}$ is

If ${\log _{10}}2 = 0.3010,$ then ${\log _5}64 =$

If the first term of an AP is 3 and the sum of its 25 terms is equal to the sum of its next 15 terms, then the common difference of this AP is

If ${H_n} = 1 + \frac{1}{2} + \frac{1}{3} + \ldots + \frac{1}{n}\;,$ then the value of ${S_n} = 1 + \frac{3}{2} + \frac{5}{3} + \ldots + \frac{{2n - 1}}{n}$ is

Let $a_1, a_2, a_3, \ldots$ be terms of an A.P. If $\frac{a_1+a_2+\ldots+a_p}{a_1+a_2+\ldots+a_q}=\frac{p^2}{q^2}, p \neq q$, then $\frac{a_6}{a_{21}}$ equals

If $H$ is the harmonic mean between $P$ and ${\cal Q}$, then the value of $\frac{H}{P} + \frac{H}{{\cal Q}}$ is

Let ${a_1},\,\,{a_2},\,\,{a_3}.......$ be an A.P. If $\frac{{{a_1} + {a_2} + ... + {a_{10}}}}{{{a_1} + {a_2} + ... + {a_p}}} = \frac{{100}}{{{p^2}}},p \ne 10,$ then $\frac{{{a_{11}}}}{{{a_{10}}}}$ is equal to

If $x, 2 x+2,3 x+3$ are in G.P., then the fourth term is

If first term of a GP is $a$, third term is $b$ and $(n+1)$ th term is $c$. The $(2 n+1)$ th term of a GP is

If ${\log _{10}}\left\{ {98 + \sqrt {{x^2} - 12x + 36} } \right\} = 2,$ then $x =$

If ${A_1},{A_2};{G_1},{G_2}$ and ${H_1},{H_2}$ be two AM’s, GM’s and HM’s between two quantities, then the value of $\frac{{{G_1}{G_2}}}{{{H_1} + {H_2}}}$

If $x, y, z$ are in GP are $\tan ^{-1} x, \tan ^{-1} y, \tan ^{-1} z$ are in A.P., then

The number of solution(s) for the equation $2 \log _x a+\log _{a x} a+3 \log _{a^2 x} a=0,$ is

If $a, b, c$ are in GP, then the equations $a x^2+2 b x+c=0$ and $d x^2+2 e x+f=0$ have a common root, if $\frac{d}{a}, \frac{e}{b}, \frac{f}{c}$ are in

If the 10th term of an A.P is $\frac{1}{{20}}$ and its 20th term is $\frac{1}{{10}}$, then the sum of its first 200 terms is

If $a,b,c,d$ are in H.P., then $ab + bc + cd =$

The value of $a^{\frac{\log _b\left(\log _b N\right)}{\log _b a}}$ is

The sum of six arithmetic means between 2 and 23 is

If $a, b, c, d$ are positive real numbers such that $a+b+c+d=2$, then $m=(a+b)(c+d)$ satisfies the relation

A G.P. consists of $2 n$ terms. If the sum of the terms occupying the odd places is $S_1$, and that of the terms in the even places is $S_2$, then $S_2 / S_1$, is

The mean of the series $a, a+n d, a+2 n d$ is

If in an increasing G.P., the sum of second and sixth term is $\frac{25}{2}$ and the product of third and fifth term is 25 , then the sum of fourth, sixth and $8^{\text {th }}$ term is

The cost and revenue functions of $a$ product are given by $C(x)=2 x+80$ and $R(x)=5 x+20$ respectively, where $x$ is the number of items produced by the manufacture. How many items the manufacturer must sell to realize some profit?

If log $\left( {x - y} \right) - \log 5 - \frac{1}{2}\log x - \frac{1}{2}\log y = 0,$ then $\frac{x}{y} + \frac{y}{x} =$

The sum of the series 5.05 $+ 1.212 + 029088 + ...\infty$ is

If the sum of $n$ terms of the series ${2^3} + {4^3} + {6^3} + ...$ is 3528, then $n$ equals to

A person is to count 4500 currency notes. Let $a_n$ denotes the number of notes he counts in the $n$th minute. If $a_1=a_2=\ldots=a_{10}=150$ and $a_{10}, a_{11}, \ldots$ are in AP with common difference $-2$, then the time taken by him to count all notes is

$\frac{1}{{3!}} + \frac{2}{{5!}} + \frac{3}{{7!}} + \ldots$ is equal to