Question

Which term of the $AP$ : $3,8,13,18,...,$ is $78$.

Answer 1

Given A.P. is $3,8,13,18,\dots$

For the above AP,

$a=3$

$d=a_2-a_1=8-3=5$

Let $n^{th}$ term of this A.P. be $78.$

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

$\Rightarrow 78=3+(n-1)5$

$\Rightarrow 75=(n-1)5$

$\Rightarrow (n-1)=15$

$\therefore n=16$

Hence, ${16}^{th}$ term of this A.P. is $78.$