Sum of First N Natural Numbers

Q.

What is the sum of the first 50 natural numbers?

1. 2550

2. 1275

3. 3000

4. 3250

Q. Question 3 (iii)
In an AP:
(iii) Given $a_{12}=37,d=3$, find a and $S_{12}$.

Q. The ${16}^{th}$ term of an AP is five times its third term. If its ${10}^{th}$ term is 41, then find the sum of its first fifteen terms.

Q.

The first term of an A.P is $2$and the common difference is $4$ The sum of its $40$ terms will be

1. $3200$

2. $1600$

3. $200$

4. $2800$

Q.

Find the sum of first 12 natural numbers without using the formula or by adding terms directly.

1. 58

2. 78

3. 48

4. 98

Q.

Find the AP whose sum to n terms is 2 $n^2$ + n.

Q.

If $9^{th}$ and ${19}^{th}$ terms of an AP are 35 and 75 respectively, then ${20}^{th}$ term is -

1. 80

2. 78

3. 81

4. 79

Q. The sum of first 50 natural numbers is

1. 1275
2. 1175
3. 51
4. none of these

Q. Question 3 (v)
In an AP:
(v) Given d = 5, $S_9=75$, find d and $a_9$.

Q. The sum of the first 18 natural numbers is .

1. 171
2. 161
3. 181
4. 188

Q.

The sum of the first 1000 positive integers is ___.

1. 50051

2. 500500

3. 50050

4. 5005

Q. Which term of the $AP$ : $3,8,13,18,...,$ is $78$.

Q. Find the sum of the first 10 natural numbers.

Q.

Find the sum of the first 18 natural numbers.

1. 171

2. 161

3. 191

4. 181

Q. In an AP:
(i) Given $a=5,d=3$, $a_n=50$, find $n$ and $S_n$.
(ii) Given $a=7$, $a_{13}=35$, find $d$ and $S_{13}$.
(iii) Given $a_{12}=37$, $d=3$, find $a$ and $S_{12}$.
(iv) Given $a_3=15$, $S_{10}=125$, find $d$ and $a_{10}$.
(v) Given $d=5$, $S_9=75$, find $a$ and $a_9$.
(vi) Given $a=2,d=8$, $S_n=90$, find $n$ and $a_n$.
(vii) Given $a=8$, $a_n=62$, $S_n=210$, find $n$ and $d$.
(viii) Given $a_n=4$, $d=2$, $S_n=-14$, find $n$ and $a$.
(ix) Given $a=3,n=8,S=192$, find $d$.
(x) Given $l=28,S=144$, and there are total 9 terms. Find $a$.

Q. Find the sum of first 20 natural numbers.

1. 210
2. 230
3. 220
4. 240

Q. what is algebraic sum?

Q. Question 3 (i)
In an AP:
(i) Given a = 5, d = 3, $a_n=50$, find n and $S_n$.

Q. Assertion : Sum of first 10 terma of the arithmetio progreasion $-0.5,-1.0,-1.5,\dots \dots \dots$ is 31 .
Reason : Sum of $n$ terma of an AP is given aa $S_n=\frac{n}{2}[2a+(n-1\left)d\right]$ where $a$ is firat term and $d$ common difference.

1. (d) Assertion (A) is false but reason (R) is true.
2. (c) Asaertion (A) is true but reason (R) is false.
   
3. (b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
   
4. (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
   

Q. Assertion : If sum of the first $n$ terma of an AP is given by $S_n=3n^2-4n$. Then ita $n^{\text{th}}$ term is $a_n=6n-7$.
Reason: $n^{\text{th}}$ term of an AP, whose sum to $n$ terma is $S_n$, is given by $a_n=S_n-S_{n}1$

1. (c) Assertion (A) is true but reason (R) is false.
   
2. (a) Both assertion (A) and reason (R) are true and reason $\left(R\right)$ is the correct explanation of assertion (A).
   
3. (d) Assertion (A) is false but reason (R) is true.
4. (b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
   

Q.

To find the sum of the first 24 terms of an AP whose $n^{th}$ term is given by $a_n=3+2n$, what is the best approach to solve this question?

1. Find the first term and the common difference.
2. List out the first 24 terms using the expression for n^th term and add them.
3. Data insufficient - we need the value of “first term” to be given.
4. Data insufficient - we need the value of “common difference” to be given.

Q. Question 11
If the sum of the first n terms of an AP is $4n-n^2$, what is the first term $\left(thatis{S}_1\right)$? What is the sum of first two terms? What is the second term? Similarly find the $3^{rd}$, the ${10}^{th}$ and the $n^{th}$ terms.

Q.

Find the sum of all odd numbers between 0 and 50.

1. 625

2. 675

3. 700

4. 650

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.

The first term of an AP is $5,$ the last term is $45$ and the sum is $400.$ Find the number of terms and the common difference.

Q. How many three-digit numbers are divisible by $7$?

Q. The $4^{th}$ term of an AP is 9 and the $9^{th}$ term of the AP is 34. The sum of the first 10 terms of the AP is ___

Q. Extending the same logic you’ve seen in the video so far, find out the sum of the first 10 natural numbers
(Consider $S_{10}=1+2+3+\dots +10$ to proceed.).

1. 110
2. 55
3. 66
4. 220
   

Q. Find the ${31}^{st}$ term of an AP whose ${11}^{th}$ term is $38$ and the ${16}^{th}$ term is $73$.

Q.

Sum of first 10 terms in 2, 4, 6, 8, ... is

1. 100

2. 98

3. 105

4. 110