Sum of n terms in AP

Q.

The value of $\frac{2}{1!}+\frac{\left(2+4\right)}{2!}+\frac{\left(2+4+6\right)}{3!}+....$ is

1. $e$

2. $2e$

3. $3e$

4. none of these

Q.

Which term of the sequence$\left(-8+18i\right),\left(-6+15i\right),\left(-4+12i\right),.....$ is purely imaginary

1. $5^{th}$term

2. $7^{th}$term

3. $8^{th}$term

4. $6^{th}$term

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. $c^2{n}^2(n+1{)}^2$

2. none of these

3. $\frac{2c^2}{3}n(n-1)(2n-1)$

4. $\frac{2}{3}{c}^{2}n(n-1)(2n-1)$

Q.

A number pattern is given by the rule $T=300-7n$. Write down the first $3$ terms

Q.

If $a_1{a}_{}......a_n$ are positive real numbers whose product is a fixed number $c$, then the minimum value of $a_1+a_2+.......+a_{(n-1)}+2a_n$ is

1. $n{\left(2c\right)}^{1/n}$

2. $(n+1)c^{1/n}$

3. $\left(2n\right)c^{1/n}$

4. $(n+1){\left(2c\right)}^{1/n}$

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. 17
4. None of these

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

1. $\frac{n}{2}log\left(\frac{a^n}{b^n}\right)$
2. $\frac{n}{2}log\left(\frac{a^{n+1}}{b^n}\right)$
3. $\frac{n}{2}log\left(\frac{a^{n+1}}{b^{n+1}}\right)$
4. $\frac{n}{2}log\left(\frac{a^{n+1}}{b^{n-1}}\right)$

Q.

Find the next term in the following sequence: a-2d, a-d, a, a+d, ...

1. a - 2d

2. 2a + 2d

3. 4a + 2d

4. a + 2d

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. $\frac{1}{2}mn(mn+1)$
2. $mn(m+1)$
3. $\frac{1}{4}mn(mn-1)$
4. None of the above

Q.

Find the sum of the first n natural numbers.

1. $\frac{n(n+1)}{2}$

2. $\frac{(n-1)(n+1)}{2}$

3. $\frac{n(n-1)}{2}$

4. $\frac{(n+1)}{2}$

Q.

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

1. 7

2. 6

3. 9

4. none of these

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. 28

3. 27

4. 25

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. 10
2. 12
3. 11
4. 13

Q.

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

1. $\frac{n}{n+1}$

2. $\frac{2n}{n+1}$

3. $\frac{2}{n(n+1)}$

4. $\frac{2(n+1)}{n+2}$

Q. The sum of n terms of two A.P. are in the ratio 5n+4:9n+6.
The ratio of their 18th terms is

1. 47:84
2. 179:321
3. 89:159
4. 2:3

Q. The value of x for which the sum $1+4+7+10+....+x=590$ is .

1. 54
2. 48
3. 58
4. 52

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

Q. The sum of all natural number between 100 and 300 which when divided by 4 leaves remainder 3 is .

1. 5025
2. 5050
3. 10050
4. 10100