Question

Let $a_{1}, a_{2} \ldots, a_{n}$ be a given $A.P$. whose common difference is an integer and $S _{ n }= a _{1}+ a _{2}+\ldots+ a _{ n }$ If $a_{1}=1, a_{n}=300$ and $15 \leq n \leq 50,$ then the ordered pair $\left( S _{ n -4}, a _{ n -4}\right)$ is equal to

• A. (2480,249)
• B. (2490,249)
• C. (2490,248)
• D. (2480,248)

Answer 1

Answer: (C)

$ a_{n} =a_{1}+(n-1) d$
$ \Rightarrow 300=1+(n-1) d $
$ \Rightarrow (n-1) d=299=13 \times 23$
$ \text { since, } n \in[15,50] $
$\therefore n =24 \text { and } d=13 $
$a_{n-4}=a_{20}=1+19 \times 13=248 $
$\Rightarrow a_{n-4}=248$
$S _{n-4}=\frac{20}{2}\{1+248\}=2490 $