Sum of n Terms of an AP

Q.

The sum of the integers from $1$ to $100$ which are not divisible by $3$ or $5$ is

1. $2489$

2. $4735$

3. $2317$

4. $2632$

Q. A man repays a loan of $₹65,000$ by paying $₹400$ in the first month and then increasing the payment by $₹300$ every month. How long will it take for him to clear the loan?

1. $24$ months
2. $24$ months
3. $20$ months
4. $12$ months

Q.

In an AP, the sum of the first ten terms is $-80$ and the sum of the next ten terms is $-280$. Find the AP.

1. $1,-1,-3,-5\dots$

2. $1,1,3,-5\dots$

3. $-1,-1,3,5\dots$

4. $-1,-1,-3,5\dots$

Q.

In an arithmetic progression, the $24th$ term is $100$. Then, the sum of the first $47$ terms of the arithmetic progression is

1. $2300$

2. $2350$

3. $2400$

4. $4700$

Q. Find the sum of first 10 odd positive integers.

1. 100
2. 81
3. 200
4. 95

Q.

A school has 3 sections each from class 1 to 12. Students of this school plant tree in the school campus to reduce air pollution. It was decided that the number of trees, that each section of each class will plant, will be the same as the class in which they are studying. How many plants were planted by the students?

1. 182

2. 78

3. 234

4. 254

Q. If 4 times the fourth term of an AP is equal to 11 times its eleventh term, then its fifteenth term is equal to:

[1 Mark]

1. 15
2. 14
3. 11
4. 0

Q. If the sum of first 10 terms of an AP is 100, then the sum of the first and the last terms is .

1. 60
2. 40
3. 20
4. 10

Q. Question 21 (iii)
Find the sum:
$\frac{a-b}{a+b}+\frac{3a-2b}{a+b}+\frac{5a-3b}{a+b}+\cdots to11terms$

Q.

Th sum of the first 30 terms of the arithmetic sequence 10, 18, 26... is ___.

1. 3880

2. 3780

3. 3680

4. 3580

Q. Question 6
The ${21}^{st}$ term of an AP whose first two terms are – 3 and 4, is

A) 17
B) 137
C) 143
D) -143

Q. Question 28
If the sum of first 6 terms of an AP is 36 and that of the first 16 terms is 256, then find the sum of first 10 terms.

Q. The sum of n terms of an arithmetic progression (AP) is $3n^2-n$.

(iii) The sum of first thirteen terms of this AP is:

[1 mark]

1. 594
2. 494
3. 484
4. 394

Q.

How many even numbers are greater than $202$ and less than $405$?

Q.

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

1. 190
2. 200
3. 210

Q. If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289, then find the common difference.

1. 2

Q. If the first term of an AP is 4 and the common difference is -4, then the term after the next term is .

1. -4
2. \N
3. 4
4. -8

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.

1. 500
2. 400
3. 300
4. 200

Q.

The $4^{\text{th}}$ term of an AP is zero. Prove that the ${25}^{\text{th}}$ term of the AP is three times its ${11}^{\text{th}}$ term.

Q. The sum of the series
${45}^2-{43}^2+{44}^2-{42}^2+{43}^2-{41}^2+{42}^2-{40}^2+\cdots \text{15 terms}$ is ___.

1. 1900
2. 2220
3. 1650
4. 1290

Q. If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289 then the common difference of the AP is

1. 1
2. 2
3. 10
4. 3

Q. Match the arithmetic progressions with their sums.

1. 10100
2. 40703
3. 10000

Q.

If $a$, $b$ and $c$ are the $1\mathrm{st},3\mathrm{rd}$ $n\mathrm{th}$ terms respectively of an AP, then prove that the sum to $n$ terms is $\frac{c+a}{2}+\frac{c^2-a^2}{b-a}$.

Q.

Find the sum to $n$ terms of the AP:
5, 2, -1, -4, -7, ...

1. $\frac{n}{2}(7+3n)$

2. $\frac{n}{2}(13-3n)$

3. $n(2-3n)$

4. $n(n-2)$

Q.

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

1. $4n+1$

2. $2n-1$

3. $3n-1$

4. $3n+1$

Q. The first and last terms of an AP are 1 and 10 respectively. If the total number of terms in the AP is 4, then $S_4$= .

1. 20
2. 11
3. 22

Q. In an AP of $n$ terms, if the first and the last terms are known, then the sum upto $n$ terms can be calculated.

1. True
2. False

Q. In the question below, there are two sentences. These two sentences are to be combined into one sentence which should convey the same meaning as conveyed by the two sentences. It is possible to combine the pair of sentences in various different ways. Beginnings of three such sentences are given below each pair of sentences. You have to find out which one, two, three or none of them is the correct, appropriate and logical way to combine the pair of sentences into one sentence to convey the same meaning as conveyed by the two sentences.
She is very simple.

1. Only A
2. Only C
3. A & B
4. A, B & C
5. A & C

Q.

How do you find the ${25}^{th}$partial sum of the arithmetic sequence ${\mathrm{a}}_1=100,{\mathrm{a}}_{25}=220$?

Q. If pth term of an AP is a and its qth term is b, then what is the sum of the first (p + q) terms of the AP? [4 MARKS]