Question

The first and the last terms of an A.P are $5$ and $45$ respectively. If the sum of all its terms is $400$, find its common difference.

• A. $d=\frac{5}{3}$
• B.
  • $d=\frac{8}{5}$
    
• C. $d=\frac{8}{3}$
• D. None of these

Answer 1

The correct option is C $d=\frac{8}{3}$

Formula,

$S_n=\frac{n}{2}[a+l]$

Given,

$a=5$

$l=45$

$S_n=400$

$400=\frac{n}{2}[5+45]$

$n=16$

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

$45=5+(16-1)d$

solving the above equation, we get,

$\therefore d=\frac{8}{3}$