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QUESTION: 1

Progressions with equal common difference are known as

Solution:

Progressions with equal common difference are known as Arithmetic Progression.

QUESTION: 2

The first term of an A.P., if its S_{n} = n^{2}+2n is

Solution:

QUESTION: 3

If the second term of an AP is 13 and its fifth term is 25, then its 7th term is

Solution:

QUESTION: 4

In an A.P., if a_{m} = 1/n and a_{n} = 1/m, then a_{mn} =

Solution:

∴ a_{mn} = a + (mn - 1) d = 1/mn + (mn - 1)

QUESTION: 5

The first term of an AP is 5, the last term is 45 and the sum is 400. The number of terms is

Solution:

QUESTION: 6

The value of ‘k’ for which the numbers x, 2x + k, 3x + 6 are in A.P. is

Solution:

QUESTION: 7

If the common difference of an A.P. is 5, then the value of a_{20 }− a_{13} is

Solution:

Given: a_{20} - a_{13} and d = 5

⇒ a_{20} - a_{13} = a + (20 - 1) d - [a + (13 - 1) d] = a + (20 - 1) x 5 - [a + (13 - 1) x 5]

⇒ a_{20 }- a_{13} - a = a + 95 - [a + 60]

= a+95 - a - 60 = 35

QUESTION: 8

Two APs have the same common difference. The difference between their 100th terms is 100, then the difference between their 1000th terms is

Solution:

QUESTION: 9

The common difference of the A.P whose S_{n} = 3n^{2}+ 7n is

Solution:

Thus, initial term of the A.P. is 5 and the common difference is 6.

QUESTION: 10

The sum of (a + b), (a – b), (a – 3b), …….. to 22nd term is

Solution:

First Term = a+b

Second Term = a-b

Common Difference is a-b-a-b = -2b.

Summation of 22 terms of an A.P. is

n/2 [ 2a + (n-1)d ]

22/2 [2 ( a+b) + (22-1)-2b ]

11 [ 2a+2a-b + (21)-2b ]

11 [ 2a+2b - 42b ]

11 [ 2a - 40b ]

22a - 40b.

So, the summation of given A.P. for 22 terms is 22a - 40b

QUESTION: 11

The next term of the A.P. √18 , √32 and √50 is

Solution:

QUESTION: 12

If 9 times the 9th term of an A.P. is equal to 11 times the 11th term , then its 20th term is

Solution:

QUESTION: 13

The 17th term of an AP exceeds its 10th term by 7, then the common difference is

Solution:

QUESTION: 14

The sum of three terms of an A.P. is 72, then its middle term is

Solution:

Let the middle term be a, then first term is a−d and next term is a+d

QUESTION: 15

The sum of odd numbers between 0 and 50 is

Solution:

Odd numbers between 0 and 50 are 1, 3, 5, 7, ………, 49 Here a = 1,d = 3−1 = 2 and

QUESTION: 16

If a, b and c are in A.P., then the relation between them is given by

Solution:

If a, b and c are in A.P., then

QUESTION: 17

The 7th term from the end of the A.P. – 11, – 8, – 5, ……., 49 is

Solution:

QUESTION: 18

The number of three digit numbers divisible by 7 is

Solution:

Three digits numbers divisible by 7 are 105, 112, 119,.........., 994

Here, a= 105, d = 112 - 105 = 7, a_{n} = 994

QUESTION: 19

The first and last terms of an A.P. are 1 and 11. If their sum is 36, then the number of terms will be

Solution:

QUESTION: 20

If 1 + 4 + 7 + ……. + k = 287, then the value of ‘k’ is

Solution:

QUESTION: 21

If the angles of a right angled triangle are in A.P. then the angles of that triangle will be

Solution:

Let the three angles of a triangle be a - d, a and a + d.

Therefore, one angle is of 60° and other is 90° (given). Let third angle be x° . then

Therefore the angles of the right angled triangle are 30°, 60°, 90°.

QUESTION: 22

The 10th term of an A.P. 2, 7, 12, …….. is

Solution:

QUESTION: 23

If a_{1 }= 4 and a_{n} = 4a_{n−1}+3, n >1, then the value of a_{4} is

Solution:

QUESTION: 24

The number of terms of the A.P. 5, 8, 11, 14, ……. to be taken so that the sum is 258 is

Solution:

QUESTION: 25

A sum of Rs.700 is to be used to award 7 prizes. If each prize is Rs.20 less than its preceding prize, then the value of the first prize is

Solution:

Let the first prize be a.

The seven prizes form an AP with first term a and common difference d = −20

Now the sum of all seven prizes = Rs. 700

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