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# Find the Common Difference and Write the Next Four Terms of Each of the Following Arithmetic Progressions: -1, 1/4, 3/2 ..... - CBSE Class 10 - Mathematics

#### Question

Find the common difference and write the next four terms of each of the following arithmetic progressions:

-1, 1/4, 3/2 .....

#### Solution

-1, 1/4, 3/2 .....

Here, first term (a1) =−1

Common difference (d)  = a_2 - a_1

= 1/4 - (-1)

=- (1 + 4)/4

= 5/4

Now, we need to find the next four terms of the given A.P

That is we need to find  a_4, a_5, a_6, a_7

So using the formula a_n = a + (n -1)d

Substituting  n = 4, 5, 6, 7 in the above formula

Substituting = 4we get

a_4 = -1 + (4 -1)(5/4)

a_4 = -1 + 15/4

a_4 = (-4 + 15)/4

a_4 = 11/4

Substituting = 5we get

a_5 = -1 + (5 - 1)(5/4)

a_5 = - 1 + 5

a_5 = 4

Substituting = 6we get

a_6 = -1 + (6 - 1)(5/4)

a_6 = -1 + 25/4

a_6 = (-4 + 25)/4

a_6 = 21/4

Substituting = 7we get

a_7 = -1 + (7 -1) (5/4)

a_7 = -1 + 30/4

a_7 = (-4 + 30)/4

a_7 = 26/4

Therefore, the common difference is d = 5/4 and the next four term are 11/4 , 4. 21/4 , 26/4`

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Solution Find the Common Difference and Write the Next Four Terms of Each of the Following Arithmetic Progressions: -1, 1/4, 3/2 ..... Concept: Arithmetic Progression.
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