Sum of 'n' Terms When 'a' and 'l' Is Given

Q. 11th term of the AP:
$-3,\frac{-1}{2},2...$ is

1. 28
2. 22
3. -38
4. -48

Q.

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

Q.

Find the sum of those integers between $1$and$500$ which are multiples of $2$as well as of $5$.

Q.

Write first four terms of the A.P. when the first term $a$ and the common difference $d$ are given as follows: $\left(iv\right)a=-1,d=\frac{1}{2}$

Q.

Find the sum of the following AP: 1, 3, 5, 7 …199.

1. 10000
2. 12000
3. 13333
4. 20000

Q.

Find the sum : 34 + 32 + 30 + .... + 10

1. 286

2. 310

3. 240

4. 300

Q. Question 10 (i)
Show that $a_1,a_2\dots \dots ,a_n,\dots \dots$ form an AP where $a_n$ is defined as below.
(i) $a_n=3+4n$
Also find the sum of the first 15 terms in each case.

Q. Question 17
Which term of the AP 53, 48, 43, …. Is the first negative term?

Q. Question 6
The first and the last term of an AP are 17 and 350 respectively. If the common difference is 9, how many terms are there and what is their sum?

Q. Question 16
The sum of first 16 terms of the AP 10, 6, 2, … is

A) -320
B) 320
C) -352
D) -400​​​​​​​

Q. Question 14
If the nth terms of the AP’s 9 , 7, 5, …. and 24, 21, 18 … are the same, then find the value of n, Also that term.

Q. Question 29
Find the sum of all the 11 terms of an AP whose middle most term is 30.

Q. Question 1
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. Question 1 (i)
Find the sum of the following APs.
(i) 2, 7, 12, …., to 10 terms

Q. Question 5
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. Find the sum of all natural numbers between $100$ and $200$ which are divisible by $4.$

1. $3600$
2. $24552$
   
3. $2357$
4. $2112$

Q. Question 10 (ii)
Show that $a_1,a_2\dots \dots ,a_n,\dots \dots$ form an AP where $a_n$ is defined as below.
(ii) $a_n=9-5n$
Also find the sum of the first 15 terms in each case.

Q. 8 terms are inserted between 5 and 43 so that the resulting sequence is an AP. The sum of the resulting AP is.

1. 240
2. 440
3. 260
4. 280

Q.

Find the sum of the first 15 multiples of 8.

1. 1000

2. 960

3. 500

4. 820

Q. Find the sum of first 51 terms of an AP whose second and third terms are 14 and 18 respectively

Q.

The sum up to $n$ terms of an AP with first term $a$, last term $l$ and common difference $d$ is

1. $\frac{n}{2}(2a+(n-1\left)d\right)$

2. $n(2a+(n-1\left)d\right)$
   

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

4. $\frac{n}{2}(a+l)d$

Q. If the first term of an AP is -8 and the common difference is 4, then the sum of the first ten terms is

1. 92
2. 96
3. 100
4. 104

Q. Find three numbers in $A.P$., whose sum is $15$ and the product is $80$.

Q. The sum up to n terms of an AP with first term $a$, last term $l$ and common difference $d$ is

1. $\frac{n}{2}(2a+(n-1\left)d\right)$
2. $n(2a+(n-1\left)d\right)$
   
3. $\frac{n}{2}(a+l)$
   
4. $n(2a+(n-1\left)d\right)$

Q. The sum up to n terms of an AP with first term $a$, last term $l$ and common difference $d$ is

1. $\frac{n}{2}(2a+(n-1\left)d\right)$
2. $n(2a+(n-1\left)d\right)$
   
3. $\frac{n}{2}(a+l)$
   
4. $n(2a+(n-1\left)d\right)$

Q. The sum up to n terms of an AP with first term $a$, last term $l$ and common difference $d$ is

1. $n(2a+(n-1\left)d\right)$
   
2. $\frac{n}{3}(2a+(n-1\left)d\right)$
3. $\frac{n}{2}(a+l)$
   
4. $n(2a+(n-1\left)d\right)$

Q.

How many multiples of $4$ lie between $10$ and $250?$

1. $80$
2. $60$
   
3. $70$
4. $90$

Q. If $a_1,a_2,a_3,........,a_{25}$ are in A.P and $a_3+a_5+a_{12}+a_{14}+a_{21}+a_{23}=60$, then $a_2+a_7+a_{19}+a_{24}=$

1. $30$
2. $40$
3. $120$
4. $180$

Q. Find three numbers in A.P . whose sum is 21 and their product is 231.

Q. Question 15
If the first term of an AP is –5 and the common difference is 2, then the sum of the first 6 terms is

A) 0
B) 5
C) 6
D) 15