Formula for sum of n terms of an AP

Q.

Find the ${20}^{\mathrm{th}}$ term from the last term of the AP: $3,8,13...,253$

Q.

The houses of a row are numbered consecutively from $1to49$. Show that there is a value of$x$ such that the sum of the numbers of the houses preceding the house numbered $x$ is equal to the sum of the numbers of the houses following it. Find this value of$x$. [Hint $S_x-1=S_{49}-S_x$ ]

Q.

The sum of all two digit odd numbers is:

1. 2530

2. 4950

3. 2475

4. 4905

Q. The sum of three numbers in AP is -3, and their product is 8. Find the numbers.

1. -4, -1, 2
2. 3, 2, 1
3. 8, 12, 16
4. 5, 6, 7

Q.

Find the sum of 20 terms of the A.P. 1, 4, 7, 10, ......

1. 590

2. 600

3. 570

4. 580

Q.

What is the sum of first $100$ natural numbers?

Q.

$\frac{1}{2.5}+\frac{1}{5.8}+\frac{1}{8.11}+...100terms$

1. $\frac{25}{160}$

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

3. $\frac{25}{151}$

4. $\frac{25}{152}$

Q.

Find the sum of 10 terms of the sequence 1, 3, 5, 7, …

1. 100

2. 98

3. 102

4. 104

Q.

In a theater, there are $20$ seats in the first row. Each row has $3$ more seats than the row ahead of it. There are $35$ rows in the theater. Find the total number of seats in the theater.

Q.

In a GP, the $3\mathrm{rd}$ term Is $24$ and the $6\mathrm{th}$ term Is $192$ then find the $10\mathrm{th}$ term.

Q.

In the given APs, find the missing terms.

$5,....,......,9\frac{1}{2}$

Q.

If the sum of p terms of an AP is qand the sum of q term is p, then the sum of p + qterms will be:

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

Q.

If a set $A=\{3,7,11,...,407\}$ and a set $B=\{2,9,16,...,709\}$ then $n(A\cap B)=$

1. $13$

2. $14$

3. $15$

4. $16$

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.

A man arranges too pay off a debt of $₹3600$ by $40$ annual instalments which form an arithmetic series.

When $30$ of the instalments are paid, he dies leaving one-third of the debt unpaid, find the value of the first instalment.

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. 104
4. 100

Q.

How many terms of the AP: 9, 17, 25, ... must be added to get a sum of 636?___

Q.

In an AP which has n terms, if we know the first and the last term, then we can find the sum of all the terms.

1. True

2. False

Q.

If $p^{th}$ term of an AP is $a$ and its $q^{th}$ term is $b$, then what is the sum of the first $(p+q)$ terms of the AP?

Q.

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

1. 300

2. 286

3. 310

4. 240

Q.

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

1. 650

2. 625

3. 675

4. 700

Q.

A spiral is made up of successive semicircles, with centers alternatively at A and B, starting with center at A, of radii 0.5 cm, 1.0 cm, 1.5 cm, 2.0 cm, ... What is the total length of such a spiral made up of thirteen consecutive semicircles?

__

Q. If the sum of the first p terms of an AP is the same as the sum of its first q terms ( where $p\ne q$ ) then show that the sum of its first $(p+q)$ terms is zero.

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.

The sum of four consecutive numbers in an A.P. with common difference $d>0$ is 20. If the sum of their squares is 120, then the middle terms are __ and __.

1. 6, 8

2. 8, 10

3. 2, 4

4. 4, 6

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

1. -64
2. -60
3. -66
4. -62

Q. 18 terms are inserted between 3 and 45 such that the resulting sequence is an AP. The sum of the resulting (finite) AP including the terms 3 and 45 is ___.

Q. The first and last terms of an AP are 1 and 5 respectively and also 5 is the 4th term of the AP. The sum of all terms of this AP is ___.