Answer
$a_{25}= 75$
Work Step by Step
$a_{n}$ of the arithmetic sequence is $a_{n} = a_{1} + (n-1)d$
Similarly,
Second term of arithmetic sequence is $a_{2} =6$
$a_{2} = a_{1} + (2-1)d$
$a_{2} = a_{1} + d$
$ a_{1} + d =6$ Equation $(1)$
Tenth term of arithmetic sequence is $a_{10} =30$
$a_{10} = a_{1} + (10-1)d$
$a_{10} = a_{1} + 9d$
$ a_{1} + 9d =30$ Equation $(2)$
Subtract Equation $(1)$ from Equation $(2)$
$ a_{1} + 9d - (a_{1} + d )=30 - 6$
$ a_{1} + 9d - a_{1} - d =24$
$8d = 24$
$d = 3$
Substituting $d$ value in Equation $(1)$
$ a_{1} + d =6$
$ a_{1} + 3 =6$
$ a_{1}= 3 $
Using $ a_{1} $ , $d$ values and $n=25$ ,
$a_{25} = a_{1} + (25-1)d$
$a_{25} = 3 + (24)3$
$a_{25} = 3 +72$
$a_{25} = 75$
