Understanding Properties of an AP from Its Algebraic Expression

Q.

Determine the AP whose $3^{rd}$ term is 5 and the $7^{th}$ term is 9.

Q.

The ${10}^{th}$ term of an AP is 52 and ${16}^{th}$ term is 82. Find the ${32}^{nd}$ term and the general term.

Q.

The eighth term of an AP is half its second term and the eleventh term exceeds one-third of its fourth term by $1.$ Find the ${15}^{th}$ term.

Q.

In the following AP's find the missing terms:
(i)-4. __, __, __, __, 6
(ii) __, 38, __, __, __, -22

Q.

The sum of the $4^{th}$ and $8^{th}$ terms of an AP is 24 and the sum of $6^{th}$ and ${10}^{th}$ terms is 44. Find the first three terms of the AP.

Q. Question 2 (iii)
Find the sum of those integers from 1 to 500 which are multiples of 2 or 5.

Q.

The ratio of the sum of n terms of two A.P.’s is $(7n+1):(4n+27)$. Find the ratio of their $m^{th}$ terms.

Q.

An AP consists of 50 terms of which the third term is 12 and the last term is 106. ${29}^{th}$ term of this AP will be ___

Q. Question 13
The $4^{th}$ term from the end of an AP – 11, –8, –5, ….., 49 is

A) 37
B) 40
C) 43
D) 58

Q.

The $n^{th}$ term of the sequence $5\times (1+6),10\times (2+6),15\times (3+6)$___ is

1. 3n(n+6)

2. n(n+6)

3. 5n(n+6)

4. 4n(n+6)

Q.

The $n^{th}$ term of the sequence $5\times (1+6),10\times (2+6),15\times (3+6)$___ is

1. n(n+6)

2. 3n(n+6)

3. 5n(n+6)

4. 4n(n+6)

Q. Arun was instructed to clap every time the count of the instructor reaches a multiple of 3. How many times did he clap when the count reacheed 63?___

Q. Let $A(-6,-5)$ and $B(-6,4)$ be two points such that a point $P$ on the line $AB$ satisfies $AP=\frac{2}{9}AB$. Find the point $P$.

1. $(-6,-3)$
2. None of these
3. $(-6,3)$
4. $(6,-3)$

Q. Arun is instructed to clap every time the count of the instructor reaches a multiple of 3. Varun is instructed to clap every time the count reaches a multiple of 7. By the time when both of them clap simultaneously for the third time, how many times did Arun clap?

1. 21
2. 25
3. 22
4. 27

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

1. -4
2. \N
3. 8
4. -16

Q. A taxi charges ₹15 for the first km and ₹8 for each additional km. The amount payable for 16 km is .

1. ₹125
2. ₹135
3. ₹145

Q. Arun was instructed to clap every time the count of the instructor reaches a multiple of 3. How many times did he clap when the count reached 63?___

Q.

An AP consists of 50 terms of which the third term is 12 and the last term is 106. Find the ${29}^{th}$ term.

___

Q. Arun is instructed to clap every time the count of the instructor reaches a multiple of 3. Varun is instructed to clap every time the count reaches a multiple of 7. They would clap at the same time when the count reaches ___

1. Multiples of 21
2. They can never clap at the same time
3. Multiples of 10
4. Multiples of 4

Q.

If terms 9, x, 21 form an arithmetic progression, then the value of x is ____.

1. 11

2. 13

3. 15

4. 17

Q.

The $n^{th}$ term of the sequence $5\times (1+6),10\times (2+6),15\times (3+6)$___ is

1. n(n+6)

2. 3n(n+6)

3. 5n(n+6)

4. 4n(n+6)

Q.

Find the next term in the following sequence: a-2d, a-d, a, a+d, ...

1. a - 2d

2. 4a + 2d

3. 2a + 2d

4. a + 2d

Q.

Find the 5th term of an arithmetic sequence whose nth term is 3n - 2.

1. 13

2. 15

3. 11

4. 17