nth term of an AP

Q. Area of the major segment = Area of the circle - Area of the minor segment

1. False
2. True

Q.

The number of terms in the series $101+99+97+...+47$ is

1. $25$

2. $28$

3. $30$

4. $20$

Q.

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.

Is 56 , a term of arithmetic sequence 3, 10, 17, .. ?

1. Yes

2. No

3. Cannot be determined

Q.

How many multiples of $9$ lie between $10$ and $300$?

Q. The 4th term of the $AP\sqrt{8},\sqrt{18},\sqrt{32}$.... is ____.

1. $5\sqrt{5}$
2. $5\sqrt{2}$
3. $3\sqrt{3}$
4. $5\sqrt{3}$

Q. The first term of an AP is 12 and the common difference is -2. Which term of the AP will be 0?

1. $6^{\text{th}}$
2. $7^{\text{th}}$
3. ${10}^{\text{th}}$
4. ${12}^{\text{th}}$

Q.

The number of terms of an A.P. Is even; the sum of the odd terms is $24$‘, of the even terms ’$30$‘, and the last term exceeds the first by ’$\frac{21}{2}$, to find the number of terms of the series.

Q. If 7 times the $7^{th}$ term of an AP is equal to 11 times its ${11}^{th}$ term, then its ${18}^{th}$ term will be

1. 7
2. 18
3. 11
4. 0

Q.

There is a finite AP of n terms such that the difference between the last and first term when divided by (n-1), gives a quotient 12 and leaves no remainder. Find the common difference of this AP.

1. 

2. 12

3. 12 x (first term)

4. 24

Q.

Two AP's have the same common difference. The difference between their ${100}^{th}$ terms is 100, what is the difference between their ${1000}^{th}$ terms?

1. 150

2. 200

3. 1000

4. 100

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.

A twenty storied building was observed from outside, each floor has a kite shaped figure which gets on magnifying as observed from the $1^{st}$ to ${20}^{th}$ floor. The area of first five kites on each floor was calculated and they were found to develop a pattern. These five areas are ${10m}^2$, ${15m}^2$ , ${20m}^2$, ${25m}^2$, ${30m}^2$ and so on. The area of the kite on the top floor is ____.

1. ${100m}^2$

2. ${110m}^2$

3. ${105m}^2$

4. ${200m}^2$

Q. If the $7^{\text{th}}$ and ${13}^{\text{th}}$ terms of an AP are 34 and 64, then its ${18}^{\text{th}}$ term is ___.

1. 87
2. 88
3. 89
4. 90

Q. Find the missing terms in the AP ___, 3, ___, -5.

1. 7, 1
2. -7, 1
3. 7, -1
4. -7, -1

Q. An AP has the first term as 2 and the common difference as 4. Which term in the AP is the first multiple of 23 to appear in the AP?

1. ${11}^{th}term$
2. ${12}^{th}term$
3. ${14}^{th}term$
4. ${35}^{th}term$

Q. The first term of an A.P. is $5,$ the common difference is $3$ and the last term is $80,$ find the number of terms.

1. $25$
2. $26$
3. $27$
4. $24$

Q. The fifth term of an AP is 25 and the ninth term is 37. The common difference of the AP will be ___.

Q. Which of the following is a term of an AP whose first term is 2 and the common difference is 4?

1. 23
2. 69
3. 46
4. 92

Q.

For what n , are the nth terms of two APs: 63, 65, 67, .. and 3, 10, 17, .. equal?

1. 10

2. 13

3. 20

4. 12

Q.

If a sequence whose $n^{th}$ term is given by
$t_n$ = 3.23 $n^2$– 4.81 n + 37, then which of the following is true?

1. The above sequence is an AP for all negative integers.

2. The above sequence is an AP only for some integers.

3. The above sequence is not an AP

4. The above sequence is an AP for all integers.

Q.

An arithmetic sequence has its $5^{th}$ term equal to 22 and its ${15}^{th}$ term equal to 62. Find the ${100}^{th}$ term

1. 400

2. 402

3. 401

4. 302

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.

Consider the following AP sequence: 134, 104, 74, … The $6^{th}$term is

1. the last positive term

2. the second negative term

3. the first negative term

4. zero

Q.

In the given series, 1.5, 0.5, -0.5, -1.5, .... , -8.5 If $n^{th}$ term is -8.5, find n.

1. 10

2. 11

3. 9

4. 12

Q.

___ multiples of 4 lie between 10 and 250.

Q. In an AP, where the first term is 7 and the common difference is 4, ___term of the AP will be five times the first term. (Enter number only)

Q. Find the numbers of integers between 50 and 500 which are divisible by 7.

1. 66
2. 65
3. 64
4. 63

Q.

Find the number of non-negative terms of the following sequence: 987, 932, 877, …

1. 17

2. 18

3. 20

4. 19

Q.

The ${17}^{th}$ term of an AP exceeds its ${10}^{th}$ term by 7. Find the common difference.

___