Sum of n Terms in AP

Q.

If the sum of a certain number of terms of the A.P. 25, 22, 19, .... is 116, Find the last term.

Q.

The largest term common to the sequences 1, 11, 21, 31, .... To 100 terms and 31, 36, 41, 46, .... to 100 terms is

1. 281

2. 381

3. 471

4. 521

Q.

$\frac{5+9+13+.......upton.terms}{If7+9+11+.....upto(n+1)terms}=\frac{17}{16}$ then n is equal to

1. none of these
2. 7
3. 6
4. 9

Q.

If the product of n positive numbers is $n^n$, then their sum is

1. never less than

2. equal to n +

3. greater than n + 2

4. always greater than + 1

Q.

In a G.P. the first, third and fifth terms may be considered as the first, fourth and sixteenth terms of an A.P. Then the fourth term of the A.P., knowing that its first term is 5 is

1. 16

2. 20

3. 12

4. 10

Q.

If a and d are two complex numbers, then the sum

to (n+1) terms of the following series

a$C_0$ - (a + d)$C_1$ + (a + 2d)$C_2$ - ........... is

1. 

2. na

3. 0

4. None of these

Q. The number of common terms to the two sequences 17, 21, 25 .......... 417 and 16, 21, 26 ....... 466 is

1. 21

2. 19

3. 20

4. 91

Q.

The 5th term of an A.P. of n terms whose sum is $n^2$ - 2n, is:

1. 76

2. 5

3. 7

4. 8

Q.

The last two digits of the number $3^{400}$ are

1. 43

2. 29

3. 01

4. 81

Q.

Fill in the blanks in following table:
$$\begin{array}{ccccc}& P\left(A\right)& P\left(B\right)& P(A\cap B)& P(A\cup B)\\ \left(i\right)& \frac{1}{3}& \frac{1}{5}& \frac{1}{15}& \cdots \\ \left(ii\right)& 0.35& \cdots & 0.25& 0.6\\ \left(iii\right)& 0.5& 0.35& \cdots & 0.7\end{array}$$

Q.

Find the value of $(0.04{)}^{{\log }_5(0.1+0.01+0.001+....)}$

__

Q.

4 HMs are inserted between 2 and 5, the 4th term in the H.P so formed is

1. 

2. 

3. 

4. 

Q.

10, 000 is larger than $(1.01{)}^{1000000}$

1. False

2. True

Q. If the sum of the series 54, 51, 48, 45.......$T_n$ is 513, then the number of terms are

1. 18
2. 20
3. None of these
4. 17

Q.

If 9 HM's are inserted between 2 & 3, the general term of i^th HM is

1. 2 - i( )

2. 2 -

3. -

4. -

Q. If sum of $n$ terms of an A.P. is $3n^2+5n$ and $T_m=164,$ then $m=$

1. 26
2. 27
3. 28
4. 25

Q. The value of $\sum _{r=1}^{n}log\left(\frac{a^r}{b^{r-1}}\right)$ is

1. 
2. 
3. 
4. 

Q.

Sum of first n terms of an A.P is $2n^2$. Find its nth term.

1. 2n-4

2. 2n-2

3. 4n - 4

4. 4n-2

Q.

If 9 AM's are inserted between 2 & 3, the general term of i^th AM is

1. -

2. 2+

3. +

4. 2 -

Q.

The value of ${\sum }_{n=1}^{2015}{i}^n$ is

1. -1

2. 2i

3. 2

4. -i

Q. If $S_1,S_2,S_3$, ..........$S_m$ are the sums of n terms of m A.P.'s whose first terms are 1, 2, 3, ........ ..... m and common differences are 1, 3, 5, .......... .2m - 1 respectively, then $S_1+S_2+S_3+........S_m=$

1. 
2. 
3. 
4. None of the above

Q. The sum of the first four terms of an A.P. is $56$. The sum of the last four terms is $112$. If its first term is $11$, then find the number of terms.

Q.

If sum of $n$ terms of an A.P. is $3n^2+5n$ and $T_m=164$, then the value of $m$ is

1. 26

2. 27

3. 28

4. 25

Q.

If the sum of n terms of an A.P is cn(n - 1), where $c>0$, the sum of the square of these terms is -

1. c²n²(n + 1)²
2. 
3. 
4. none of these

Q.

Find the sum of the first 15 terms of the series 3 + 5 + 7 + 9 +. . . . . . n terms.___

Q.

Find the sum of the first n natural numbers.

1. 

2. 

3. 

4. 

Q.

The sum of (n+1) terms of $\frac{1}{1}+\frac{1}{1+2}+\frac{1}{1+2+3}+..........$ is

1. 

2. 

3. 

4. 

Q. If the sum of the first 2n terms of the A.P. 2, 5, 8, ...., is equal to the sum of the first n terms of the A.P. 57, 59, 61, ...., then n equals

1. 12
2. 11
3. 13
4. 10

Q.

Harikiran purchased a house in Rs. 15000 and paid Rs. 5000 at once. Rest money he promised to pay in annual instalment of Rs. 1000 with 10% per annum interest. How much money is to be paid by him

1. Rs. 21555

2. Rs. 20475

3. Rs. 20500

4. Rs. 20700