Sum of 'n' Terms of an Arithmetic Progression

Q.

If $\frac{(b+c-a)}{a},\frac{(c+a-b)}{b},\frac{(a+b-c)}{c}$ are in $AP$, then $a,b,c$ are in

1. $G.P.$

2. $A.P.$

3. $H.P.$

4. $A.G.P.$

Q.

If the sum of the first 14 terms of an AP is 1050 and its first term is 10, find the ${20}^{th}$ term.

__

Q.

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

1. $\frac{1}{6}$

2. $\frac{1}{5}$

3. $\frac{1}{4}$

4. $\frac{1}{7}$

Q. Question 7
Find the sum of first 22 terms of an AP in which d = 7 and ${22}^{nd}$ term is 149.

Q.

The sum of the first three terms of an AP is $33$. If the product of the first and the third terms exceeds the second term by $29$, then find the AP.

Q.

How many terms of the AP 27, 24, 21, ..... are required to get the sum as 0?

1. 19

2. 24

3. 17

4. 27

Q. Question 8
Which term of an AP : 21, 42, 63, 84, …. is 210?

A) $9^{th}$
B) ${10}^{th}$
C) ${11}^{th}$
D) ${12}^{th}$

Q.

If $a_m$ denotes the $mth$ term of an A.P then $a_m$

1. $\frac{2}{(a_{m+k}+a_{m-k})}$

2. $\frac{(a_{m+k}–a_{m-k})}{2}$

3. $\frac{(a_{m+k}+a_{m-k})}{2}$

4. None of these

Q. Consider the following AP:

24, 21, 18.....

How many terms of this AP must be taken so that their sum is 78? [4 MARKS]

Q.

If $\text{A}$ and $\text{B}$ are two independent events such that $\text{P(A) = 0.40, P(B) = 0.50.}$ Find $\text{P(neither A nor B)}$

1. $0.90$

2. $0.10$

3. $0.2$

4. $0.3$

Q. Question 7
If the $2^{nd}$ term of an AP is 13 and $5^{th}$ term is 25, what is its $7^{th}$ term?

A) 30
B) 33
C) 37
D) 38

Q.

The sum of the first five terms of an AP and the sum of the first seven terms of the same AP is $167$. If the sum of the first ten terms of this AP is $235$, find the sum of its first twenty terms.

Q.

What is the sum of first 30 multiples of 4?

1. 1880

2. 1860

3. 1800

4. 1660

Q. the sum of the first n terms of an AP is $(\frac{5n^2}{2}+\frac{3n}{2})$. Find the nth term and the 20th term of this AP.

Q.

Find the sum to 100 terms of the series 1 + 4 + 7 + 5 + 13 + 6.........

1. 8825

2. 9825

3. 10825

4. 7825

Q.

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

1. 330
2. 255
3. 285
4. 560

Q. Question 26
If $S_n$ denotes the sum of first n terms of an AP, then prove that $S_{12}=3(S_8-S_4)$

Q. Question 12
If 7 times the $7^{th}$ term of an AP is equal to 11 times its ${11}^{th}$ term, then its ${18}^{th}$ term will be

A) 7
B) 11
C) 18
D) 0

Q. Question 21 (i)
Find the sum:
1 + (-2) + (-5) + (-8) + . . . + (-236)

Q.

The sum of $r$ terms of an AP is $2r^2+3r.$ The $n^{\text{th}}$​ term is ___.

1. $2n-1$

2. $3n-1$

3. $4n+1$

4. $3n+1$

Q.

The sum of all the 3 sides of a triangle is called__.

Q. Question 7
Find the sum of first 22 terms of an AP in which d = 7 and ${22}^{nd}$ term is 149.

Q. Find the sum to 100 terms of the series:
1 + 4 + 7 + 5 + 13 + 6 ...

1. 7825
2. 8825
3. 9825
4. 10825

Q. The sum of first ten terms of an AP is four times the sum of its first five terms. What is the ratio of first term and common difference?

1. 1
2. 1 : 2
3. 4
4. 1 : 4

Q.

The sum of the first 20 terms of an AP is 1280, and the common difference is 20. Then the fourth term of the AP will be __.

1. -60

2. -64

3. -62

4. -66

Q.

Find the sum of the AP:$-37,-33,-29,...$ upto $12$ terms.

Q. If the sum of the first p terms of an AP is qand that of q terms is p, then the sum of the first (p + q)terms will be:

1. 0
2. p - q
3. p + q
4. -(p + q)

Q.

Find the sum of the following AP: $\frac{1}{15},\frac{1}{12},\frac{1}{10},...$ to $11$ terms

Q. The sum of four consecutive numbers in an AP is 32 and the ratio of the product of the first and the last term to the product of two middle terms is 7 : 15. Find the numbers.

Q. The sum of first ten multiples of 6 lying between 100 and 300 is equal to:

[1 Mark]

1. 258
2. 290
3. 1, 290
4. 2, 190