Question

Determine the number of terms in the $A.P.3,7,11,...,407$. Also, find its $20^{th}$ term from the end.

• A. $102,331$
• B. $101,330$
• C. $100,331$
• D. $100,399$

Answer 1

Answer: (A)

Here, first term $a=3$ and common difference $d=4$.
Let there be $n$ terms in the given $A.P$. Then,
$n^{th}$ term $=407$
$\Rightarrow 407=3+(n-1)\times 4$
$\Rightarrow n=102$
So, there are $102$ terms in the given $A.P$.
Now, $20^{th}$ term from the end
$=[102-20+1{]}^{th}$ term from the beginning
$=83^{rd}$ term from the beginning
$=3+(83-1)\times 4=331$