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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`

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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
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