Question

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

• A. $t_{16}$
  
• B. $t_{18}$
• C. $t_{14}$
• D. None of these
  

Answer 1

The correct option is A $t_{16}$

Given :- A.P. is $3,8,13,18,....$

To get :- which term is $78$.

solution :-

First term $=3=a_1$

common diff. $=d=(8-3)=(13-8)=(18-13)=5$

$\therefore$ Let the required term be n

$\therefore a_n=78$

$\therefore a_n=a_1+(n-1)d$

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

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

$\Rightarrow 78=3+5n-5$

$\Rightarrow 78=-2+5n$

$\Rightarrow 5n=78+2=80$

$\Rightarrow 5n=80$

$\Rightarrow n=16$

$\therefore$ so the required term is ${16}^{th}$ term.

i.e. $t_{16}$