Question

If a is the nth term of an AP and a19-a13=24,the common difference is?​

Answer 1

a19 - a13 = 24

so, a + 18d - (a + 12d) = 24

a + 18d - a - 12d = 24

6d = 24

d = 24/6

d = 4

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Answer 2

Given:

'a' is the nth term of an AP and $a_{19} - a_{13} = 24$

To find:

The common difference of an AP

Solution:

The general term of the AP is given as,

$t_n = a + (n-1) d$

If a is the nth term of an AP and $a_{19} - a_{13} = 24$

Then,

$a_{19} = a + (19-1)d$

$a_{19} = a + 18d$

$a_{13} = a + (13-1)d$

$a_{13} = a + 12d$

$a_{19} - a_{13} = 24$

Therefore,

$a_{19} - a_{13} = a + 18d -(a+12d)$

$a + 18d -a-12d =24$

6d = 24

d = $\frac{24}{4}$

d = 4

The common difference is 4

Final answer:

The common difference of an given AP is 4