Terms in an Arithmetic Progression

Q.

What is the difference between arithmetic mean and geometric mean?

Q.

What is the arithmetic mean of the numbers $a$ and $b$?

1. = GH

2. = AH

3. = AG

4. = AG

Q. In an AP, the first term is −4, the last term is 29 and the sum of all its terms is 150. Find its common difference. [CBSE 2011]

Q.

Find the arithmetic mean of given numbers

4, 8, 12, 16, 20, 24.

1. 14

2. 18

3. 16

4. 12

Q.

Find the sum to $n$ terms of the AP:
5, 2, -1, -4, -7, ...

1. $\frac{n}{2}(7+3n)$

2. $\frac{n}{2}(13-3n)$

3. $n(2-3n)$

4. $n(n-2)$

Q. Find the common difference of the A.P 1, -2, -5, -8, ....

1. -1
2. -2
3. -3
4. -4

Q. Find the 10th term of the AP 3, 6, 9, .....

1. 30
2. 33
3. 36
4. 39

Q.

Which of the following is/are correct for an AP whose common difference is d.

1. If d$<$0, then AP is increasing

2. If d$>$0, then AP is decreasing.

3. If d = 0, then all the terms of AP are the same.

4. None of the above is correct.

Q.

What are the conditions for a sequence to be an AP?

1. Division between two consecutive numbers should be same.

2. Difference between two consecutive numbers should be same.

3. Multiplication between two consecutive numbers should be same.

4. Division between two consecutive numbers should be same.

Q.

Find the next two terms of the A.P.:- -10, -6, -2…

1. 2, 6

2. -4, -8

3. 4, 8

4. 6, 10

Q. Find the sum of the first 10 terms of the AP : 5, 9, 13, . . .

1. 205
2. 230
3. 255
4. 270

Q.

If a, b, c are in arithmetic progression , then show that the following are in arithematic progression :-

1. b+c , c+a , a+b

2. a+3k , b+3k , c+3k

3. a\7k , b\7k , c\7k

4. b+c-a , c+a-b , a+b-c

Q.

Question 36

$4.7÷100=$ ___.

Q.

Select the set of numbers that forms an AP.

1. 1, 3, 5, 7, ...

2. 1, 4, 5, 8, ...

3. 0, 1, 3, 5, ...

4. 2, 4, 6, 8, ...

Q. Question 2
y+3 =10

Q. Find the common difference of the A.P. and write the next two terms:

(i) 51, 59, 67, 75, ..

(ii) 75, 67, 59, 51, ...

(iii) 1.8, 2.0, 2.2, 2.4, ...

(iv) $0,\frac{1}{4},\frac{1}{2},\frac{3}{4},...$

(v) 119, 136, 153, 170, ...

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

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

Q. The fourth rerm from the end of the Ap:-11, -8, -5, _ 49 is

Q. { 17. If the }10 th term of an }AP is }52 and the }17 th term is }20 more than the }13 th }} term, find the AP.

Q. Find the value of x for which (8x + 4), (6x - 2) and (2x + 7) are in A.P.

1. 
   15
2. 
   7.5
3. 
   21
4. 
   43

Q. Which term of the A.P. -2, -7, -12, ... will be equal to -77? Find the sum of the terms upto -77.

1. -630
2. -627
3. -632
4. -615

Q. 1, -2, -5, -8, ...
The common difference of the given A.P is .

1. -1
2. 2
3. -3

Q. Given that p, q, r, s are in an arithmetic progression, which of the following condition(s) can be used to verify this?

1. p - q = s - r
   
2. p + q + r + s = 0
   
3. p + q = r + s
4. q - p = s - r

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

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

Q. Write the next term of the AP $\sqrt{2},\sqrt{8},\sqrt{18},......$

Q. Given that p, q, r, s are in an arithmetic progression, which of the following condition(s) can be used to verify this?

1. p - q = s - r
   
2. p + q + r + s = 0
   
3. p + q = r + s
4. q - p = s - r
   

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

Q. Very-Short and Short-Answer Questions

What is the 5th term from the end of the AP 2, 7, 12, ..., 47? [CBSE 2011]

Q. Find the 11th term of the AP 8, 10, 12, 14, ...

1. 24
2. 26
3. 28
4. 30

Q.

An AP has first term -3 and a common difference -1. Find the 3^rd term of the A.P.

1. -5

2. -1

3. -7

4. 5