Arithmetic progressions - common difference of Arithmetic progressions for class 10 maths

Chapter : Arithmetic Progressions Website: www.letstute.com

Arithmetic Progressions

Problems based on Arithmetic Progressions



Q) How many terms of two digits are divisible by 3 ?

Solution:

Let n be number of terms in this AP

Two digits numbers divisible by 3 are 12, 15, 18, 21,…. 99

These numbers form an AP whose first term a = 12 and common difference d = 3.

Then an = 99

a + (n - 1)d = 99

12 + (n - 1) (3) = 99

12 + 3n - 3 = 99



Hence , there are 30 numbers of two digits which are divisible by 3

3n = 90

n = 30



Q) How many multiples of 4 lie between 10 and 250 ?

Solution:

Let the number of terms in this AP be n.

Multiples of 4 between 10 and 250 are 12, 16, 20, …248

These numbers form an AP whose first term a = 12 and common difference d = 4.

Then an = 248

a + (n - 1)d = 248

12 + (n - 1) 4 = 248

4n - 4 = 236



Hence , there are 60 multiples of 4 that lie between 10 and 250.

4n = 240

n = 60



Q) How many three digit numbers are divisible by 7 ?

Three digit numbers divisible by 7 are 105, 112, 119,…, 994. These numbers form an AP whose first term a = 105 and common difference = 7.

Let n be the number of terms in this AP

Then an = 994

a + (n - 1)d = 994

105 + (n - 1) 7 = 994

Solution:



Hence , there are 128 three digit numbers that are divisible by 7.

7n – 7 = 889

7n = 896

n = 128

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Arithmetic progressions - common difference of Arithmetic progressions for class 10 maths