Question

If the common difference of an AP is 5,then what is a18-a13?(a) 5,(b) 20,(c) 25,(d) 30​

Answer 1

Heya!!

An = a + ( n -1 ) d

d = 5 { Given }

Here a is ist term and d is common Difference.

A18 = a + ( 18 - 1 ) ×5

A18 = a + 17×5

And

A13 = a + ( 13 -1 ) ×5

A13 = a + 12 ×5

So,

A18 - A13 = a + 85 - a - 60

A18 - A13 = 25.

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Answer 2

Given:

The common difference of an AP is 5.

To find:

a18 - a13.

Solution:

As we know that the nth term of an AP that has a = first term, d = common difference and n = number of terms till the nth term is given by using the formula:

${n}^{th} \: term = a + (n - 1)d$

Now,

as given, we have

Common difference = 5

So,

18th term of the AP or a18

$= a + 17d$

(as n = 18)

Similarly,

13th term of the AP or a13

$= a + 12d$

(as n = 13)

So,

a18 - a13

$= a + 17d - (a + 12d)$

$= 5d$

$= 5 (5)$

$= 25$

Hence, the value of a18 - a13 is (c) 25.