Question

1 + 4 + 7 + .... + x = 287 find the value of x

• A. x = 20.
• B. x = 40.
• C. x = 10.
• D. x = 30.

Answer 1

The correct option is B x = 40.

Series is $1+4+7+.....+x$

which is in A.P. where

First term, $a=1$

and Common difference, $d=a_2-a_1=4-1=3$

Let total no. of terms is $n$

Sum of n terms, $S_n=287$

$S_n=\frac{n}{2}\{2a+(n-1)d\}$

So,

$\frac{n}{2}\{2\left(1\right)+(n-1)3\}=287$

$n\{2+3n-3\}=574$

$3n^2-n=574$

$3n^2-n-574=0$

$3n^2-42n+41n-574=0$

$n=14$ or $n=-\frac{41}{3}$

$n$ cannot be negative so $n=14$

Now $x$ is the $n$th term.

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

$=1+13\left(3\right)=40$