Question

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

• A. ${16}^{th}$
• B. ${15}^{th}$
• C. ${17}^{th}$

Answer 1

The correct option is A ${16}^{th}$

Here, First term, $a=3$

Common difference, $d=8-3=5$
$a_n=78$
Using formula $a_n=a+(n-1)d$ to find nth term of arithmetic progression, we get
$a_n=3+(n-1)5$ {we want to find value of n here.}
$\Rightarrow 78=3+(n-1)5$
$\Rightarrow 75=5n-5$
$\Rightarrow 80=5n$
$\Rightarrow n=\frac{80}{5}=16$
It means ${16}^{th}$ term of the given AP is equal to 78.