Find the common difference the following A.P
$1, 4, 7, 10, 13, 16, . .$

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Solution

Given series is $1, 4, 7, 10, 13, 16, . . . . . . .$

Common difference can be found out as : $c . d . = a_{2} - a_{1} = a_{3} - a_{2} = a_{4} - a_{3} = . . .$

Let's check, therefore,

$a_{2} - a_{1} =$

$4 - 1 = 3$
Also,

$a_{3} - a_{2} =$

$7 - 4 = 3$

And,

$a_{4} - a_{3} =$

$10 - 7 = 3$
$∴$ common difference $(d) = 3$

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