# Find the Common Difference and Write the Next Four Terms of the Following Arithmetic Progressions: -1, (-5)/6, (-2)/3 - Mathematics

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

-1, (-5)/6, (-2)/3

#### Solution

-1, (-5)/6, (-2)/3

Here, first term (a1) =−1

Common difference (d)  = a_2 - a_1

= -5/6 - (-1)

= (-5 + 6)/6

= 1/6

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) (1/6)

a_4 = -1 + (1/2)

a_4 = (-2 + 1)/2 = (-1)/2

Substituting = 5we get

a_5 = -1 + (5 -1)(1/6)

a_5 = - 1 + 2/3

a_5 = (-3 + 2)/3

a_5 = - 1/3

Substituting = 6we get

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

a_6 = -1 + 5/6

a_6 = (-6 + 5)/6

a_6 = - 1/6

Substituting = 7we get

a_7 = -1 + (7 -1) (1/6)

a_7 = -1 + 1

a_7 = 0

Therefore, the common difference is d = 1/6 and the next four terms are -1/2, -1/3, -1/6,0`

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#### APPEARS IN

RD Sharma Class 10 Maths
Chapter 5 Arithmetic Progression
Exercise 5.3 | Q 4.4 | Page 11