Sum of n Terms in GP

Q.

Sum the series 5 + 55 + 555 + ... to n terms.

Q.

Find the sum to n terms of the sequences 8, 88, 888, 8888 ....

Q.

Find the sum of first 10 terms of the G.P 3, 6, 12, 24 ..........

Q. If cos x +cosy = $\frac{1}{3}$, sin x + sin y = $\frac{1}{4}$ then sin (x + y) =

1. 
2. 
3. 
4. 

Q.

The number of ways in which 2n different things can be divided equally into two distinct groups is $\frac{2n!}{(n!{)}^2}$ (If order of the group is important)

1. True

2. False

Q.

Sum of n terms of series 12 + 16 + 24 + 40 +......... will be

1. 

2. 

3. 

4. 

Q.

The sum of series 1.2.4 + 2.3.5 + 3.4.6 + ----------- 20 terms.

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Q.

Find the sum of first 10 terms of the G.P 3, 6, 12, 24 ..........

__

Q.

$Therangeofthefunctionf\left(x\right)=co{s}^2\frac{x}{4}+sin\frac{x}{4},xϵRis$

1. 

2. 

3. 

4. 

Q.

$\underset{x\to 0}{lim}\frac{1-cosxcos2xcos3x}{si{n}^{2}2x}$ is equal to

1. 7/2

2. 7/3

3. 7/4

4. 7/5

Q.

If $(a-d{)}^2$ , $a^2$ , $(a+d{)}^2$ are in GP, then $\frac{d^2}{a^2}$ equals to [a ≠ 0, d ≠ 0]

1. 1

2. 2

3. 3

4. 4

Q.

Write the first five terms of the sequences whose $n^{th}$ term is:

$a_n=\frac{n}{n+1}$

Q.

Find the indicated terms in each of the sequences in where $n^{th}$ terms are :

$a_n=\frac{n^2}{2^n};a_7$

Q. If $(10{)}^9+2(11{)}^1(10{)}^8+3(11{)}^2(10{)}^7+...+10(11{)}^9=k(10{)}^9,$ then k is equals to:
(IIT JEE Main 2014)

1. $\frac{121}{10}$
2. $\frac{441}{100}$
3. 110
4. 100

Q.

Find the sum to n terms

$1\times 2+2\times 3+3\times 4+4\times 5+\dots \dots$

Q.

If $(10{)}^9+2(11{)}^1(10{)}^8+3(11{)}^2(10{)}^7+...+10(11{)}^9=k(10{)}^9,$ then k is equals to:
(IIT JEE Main 2014)

1. $\frac{121}{10}$

2. $\frac{441}{100}$

3. 100

4. 110

Q.

If $-\frac{\pi }{2}<x<\frac{\pi }{2}$ and the sum to infinite number of terms of the series$cosx+\frac{2}{3}cosxsi{n}^{2}x+\frac{4}{9}cosxsi{n}^{4}x+.....$ is finite, then $x$ lies in the set

1. 
2. 
3. 
4. 

Q.

How many terms of the series 3, 9, 27 . . . . . . . will add up to 363?

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Q. State whether each of the following statement is true or false. Justify your answer.
(i) {$2,3,4,5$} and {$3,6$} are disjoint sets.
(ii) {$a,e,i,o,u$} and {$a,b,c,d$} are disjoint sets
(iii) {$2,6,10,14$} and {$3,7,11,15$} are disjoint sets
(iv) {$2,6,10$} and {$3,7,11$} are disjoint sets

Q.

Find the indicated terms in each of the sequences where $n^{th}$ term is :

$a_n=(-1{)}^{n-1}{n}^3;a_9$

Q.

$1+2^1+2^2+2^3.........{.2}^{1999}$ =

1. 

2. 

3. 

4. 

Q.

Write the first five terms of the sequences whose $n^{th}$ term is :

$a_n=2^n$

Q. The sum of the first 20 term of the sqeuence 0.7, 0.77, 0.777, ...., is
(IIT JEE Main 2013)

1. $\frac{7}{9}(99+{10}^{-20}$
2. $\frac{7}{81}(179-{10}^{-20}$
3. $\frac{7}{9}(99-{10}^{-20}$
4. $\frac{7}{81}(179+{10}^{-20}$

Q. $5^2+6^2+7^2+...+{20}^2$

Q.

If the sum of the n terms of G.P. is S product is P and sum of their inverse is R, than $P^2$ is equal to

1. 

2. 

3. 

4. 

Q.

$1+2^1+2^2+2^3.........{.2}^{1999}$ =

1. 

2. 

3. 

4. 

Q. The sum of the series 6 + 66 + 666 + ........ upto n terms is

1. (10^{n - 1} - 9n + 10)/ 81
2. None of these
3. 2(10^{n + 1} - 9n - 10)/ 27
4. 2(10ⁿ - 9n - 10)/ 27

Q.

Find the sum of first 10 terms of the G.P 3, 6, 12, 24___

Q.

$1+2^1+2^2+2^3.........{.2}^{1999}$ =

1. 

2. 

3. 

4. 

Q. How many terms of G.P $3,3^2,3^3,...$ are needed to give the sum $120$?