Recent questions tagged sequences-and-series

If $S_{n}=\frac{1}{6}\;n\;(2n^2+9n+13)\;$, then $\sum_{r=1}^n\;\sqrt{a_{r}}\;$ equals.

asked Jan 20, 2014 by yamini.v

1 answer

Sum of series $\;\frac{1}{2}+\frac{3}{4}+\frac{7}{8}+\frac{15}{16}+.....\;is:$

asked Jan 20, 2014 by yamini.v

1 answer

If $f\;(xy)=f\;(x+y)\;\forall\;x,y\;\in\;R$ and $\;f\;(2009)=2009$, then $f\;(-2009)$ equals

asked Jan 20, 2014 by yamini.v

1 answer

Sum of n terms of series $\;\frac{1}{1^3}\;+\frac{1+2}{1^3+2^3}\;+\frac{1+2+3}{1^3+2^3+3^3}\;+....\;is$

asked Jan 20, 2014 by yamini.v

1 answer

If x, y, z > 1 are in GP, then $\frac{1}{1+lnx}$, $\frac{1}{lny}$, $\frac{1}{lnz}$ are in

asked Jan 20, 2014 by yamini.v

1 answer

If in an AP , $\;m^{th}$ term is $\;\frac{1}{n}$ and $\;n^{th}\;term\;is\frac{1}{m}$ , then $\;mn^{th}$ term is :

asked Jan 20, 2014 by yamini.v

1 answer

Let $S_{1}, S_{2}$....be the squares such that for each $n\geq\;1$, the length of side of $S_{n}$ = length of diagonal of $S_{n+1}$. If side of $S_{1}$ is 20 cm, the smallest value of n such that area of $S_{n}\;<\;2$ is

asked Jan 20, 2014 by yamini.v

1 answer

If $a, b, c$ are in AP and $a^2$, $b^2$, $c^2$ in GP, and $a+b+c=\frac{3}{2}$, then value of $c$ is

asked Jan 20, 2014 by yamini.v

1 answer

If $(1+3+5+....+p)$+$(1+3+5+....+q)$ = the smallest value of $p+q+r, (p>6)$ is

asked Jan 20, 2014 by yamini.v

1 answer

Sum of series $S$ = $\frac{1}{2}$+$\frac{1}{3}\;(1+2)$+$\frac{1}{4}\;(1+2+3)$+$\frac{1}{5}\;(1+2+3+4)$+......upto 20 terms is

asked Jan 20, 2014 by yamini.v

1 answer

Sum of series $1^2$-$2^2$+$3^2$-$4^2$+$5^2$+.....+$1001^2$ is

asked Jan 20, 2014 by yamini.v

1 answer

If the $\;10^{th}\;$ term of a $GP$ is $9$ and the $\;4^{th}\;$ term is $4$, then the $\;7^{th} \;$term is

asked Jan 19, 2014 by yamini.v

1 answer

In an AP, the $\; 4^{th}\;$ term is $36$. The$\; 21^{st}\;$ term is $108$ more than the $\;9^{th}\;$ term. What is the first term a and the common difference $d$?

asked Jan 19, 2014 by yamini.v

1 answer

The sum of 0.2, 0.22, 0.222, 0.2222.....till n terms is given by

asked Jan 18, 2014 by yamini.v

2 answers

The sum of $n$ terms of an arithmetic progression is $\;n\;(2n-1)$. What is the $m^{th}$ term of the series?

asked Jan 18, 2014 by yamini.v

1 answer

If a, g and h are the AM, GM and HM respectively of two positive numbers x and y, then identify the correct statement.

asked Jan 18, 2014 by yamini.v

1 answer

The sum of n terms of two APs is in the ratio$\; 5n + 1: 4n+10$. Find the ratio of their $\;5^{th}$ terms.

asked Jan 18, 2014 by yamini.v

1 answer

The number of terms in the AP a, b,....c is

asked Jan 17, 2014 by yamini.v

1 answer

A train travels from A to B at speed of x km/hour and from B to A at speed of y km/hour. The average speed of the train from A to B and back to A, would be calculated by the

asked Jan 17, 2014 by yamini.v

1 answer

If three numbers are in GP, then their logarithms will be in

asked Jan 17, 2014 by yamini.v

1 answer

The sum of three decreasing numbers in AP is 27. If -1, -1, and 3 are added to them respectively the resulting series is in GP. The numbers are

asked Jan 17, 2014 by yamini.v

1 answer

The $n^{th}$ term of series is $\frac{1}{1}$, $\frac{(1+2)}{2}$, $\frac{(1+2+3)}{3}$......is

asked Jan 17, 2014 by yamini.v

1 answer

Sum of squares of first n natural numbers exceeds their sum by 330, then n =

asked Jan 17, 2014 by yamini.v

1 answer

If a, b and c are in H.P, then a/(b+c), b/(c+a), c/(a+b) are in

asked Jan 17, 2014 by yamini.v

1 answer

If arithmetic, geometric and harmonic means between two positive real numbers is A, G and H respectively, then, which of the following is true?

asked Jan 17, 2014 by yamini.v

1 answer

The sum of n terms of the infinite series $1.3^2$+$2.5^2$+$3.7^2$+-------$\infty$ is given by

asked Jan 17, 2014 by yamini.v

1 answer

Ram shares a photo link on facebook with 3 persons and requests each of them to share with 3 more persons and continue the chain. For every share of the photo link if Rs 100 is donated to the Adyar Cancer society, what is the total amount collected by the society till the $b^{th}$ set of shares.

asked Jan 6, 2014 by yamini.v

1 answer

Given $4$ numbers, the first $3$ numbers are in $AP$ and the last $3$ numbers are in $GP$. The $1^{st}$ and $3^{rd}$ terms add upto $2$ and the $2^{nd}$ and $4^{th}$ terms add to $17$. Find the numbers.

asked Jan 6, 2014 by yamini.v

1 answer

If $a, b, c$ are in $AP, a, x, b$ and $b, y, c$ in $GP$, what is the progression type for $x^2,b^2,y^2$?

asked Jan 6, 2014 by yamini.v

1 answer

Find the sum of the series upto 20 term 1+(1+2)+(1+2+3)+--------

asked Jan 6, 2014 by yamini.v

1 answer

Find the sum of 8 terms of the series whose $n^{th}$ term is given by $n^2+2^n$

asked Jan 6, 2014 by yamini.v

1 answer

For what value of n , the $n^{th}$ term of the GPs 2560,1280,640 ----- and 10,20,40 ------ are equal.

asked Jan 6, 2014 by yamini.v

1 answer

The first term of a $GP$ is $4$ and the sum of its $3^{rd}$ and $5^{th}$ terms is $360$. Find the common ratio.

asked Jan 6, 2014 by yamini.v

1 answer

Find three numbers in AP whose sum is 33 and the sum of whose squares is 395

asked Jan 6, 2014 by yamini.v

1 answer

Two cars start at a point A at the same time. The first car goes with a uniform speed of 100 Km/hr and the second car starts at 80 for the first hour and increases the speed by 10 km/hr every hour. After how much time does the second car overtake the first car, assuming these are no stops in between.

asked Jan 6, 2014 by yamini.v

1 answer

Given an AP, if the sum of first 5 terms is 175 and the sum of first 10 terms is 700, find the sum of the first 7 terms.

asked Jan 6, 2014 by yamini.v

1 answer

Find the sum of all natural numbers between 45 and 300 that are exactly divisible by 7.

asked Jan 5, 2014 by yamini.v

1 answer

How many 3 digit numbers leave a remainder of 2 when divided by 7 ?

asked Jan 5, 2014 by yamini.v

1 answer

How many 3 digit numbers are divisible by 5?

asked Jan 5, 2014 by yamini.v

1 answer

How many two digit numbers are divisible by 4?

asked Jan 5, 2014 by yamini.v

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Which term of the sequence 130,126,122----- is the first negative term.

asked Jan 5, 2014 by yamini.v

1 answer

Find the value of $n$ such that the $n^{th}$ term of the sequences 27,24,21------- and 2,4,6----- are equal.

asked Jan 5, 2014 by yamini.v

1 answer

The $n^{th}$ term of a progression is $2n+3$. What is the type of progression and what is its $15^{th}$ term.

asked Jan 4, 2014 by yamini.v

1 answer

For what value of n is $\frac{a^{n+1}+b^{n+1}}{a^n+b^n}$ the GM of 4 and 16.

asked Jan 3, 2014 by yamini.v

1 answer

Find the value of n such that $\frac{5^{(n+1)}+17^{(n+1)}}{5^n+17^n}$ is the AM of 5 and 17

asked Jan 3, 2014 by yamini.v

1 answer

Given that $a\;\xi\;b$ are not equal , find the value of n so that $\frac{a^{n+1}+b^{n+1}}{a^n+b^n}$ is the GM of $a\;\xi\;b$

asked Jan 3, 2014 by yamini.v

1 answer

If n arithmetic means are interested between $0$ and $32$ such that the $2^{nd}$ mean is one-seventh of the $(n-1)^{th}$ mean, find the value of $n$.

asked Jan 3, 2014 by yamini.v

1 answer

Insert k arithmetic means between 1 and $k^2$ . what is the resulting series?

asked Jan 3, 2014 by yamini.v

1 answer

In the series 2,10,50 ------ the number of terms required to make a sum of 7812 is

asked Jan 3, 2014 by yamini.v

1 answer

Which term of the series $\frac{16}{9}$, $\frac{4}{3}$, $1$, $\frac{3}{4}$------is $\frac{243}{1024}$

asked Jan 3, 2014 by yamini.v

1 answer

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