Solve for x : 1 + 4 + 7 + 10 + … + x = 287. - Vidyadip

Question

Solve for x : 1 + 4 + 7 + 10 + … + x = 287.

✓

Answer

$
1+4+7+10+\ldots+x=287
$
Here, $a=1, d=4-1=3, n=x$
$I=x=a=(n-1) d=1+(n-1) \times 3$
$\Rightarrow x -1=( n -1) d$
$S _{ n }=\frac{n}{2}[2 a+(n-1) d]$
$287=\frac{n}{2}[2 \times 1+(n-1) 3]$
$574=n(2-3 n-3)$
$\Rightarrow 3 n^2-n-574=0$
$\Rightarrow 3 n^2-42 n+41 n-574=0$
$\Rightarrow 3 n ( n -14)+41( n -14)=0$
$\Rightarrow(n-14)(3 n+41)=0$
Either $n-14=0$,
then $n=14$
or
$
3 n+41=0 \text {, }
$
then $3 n=-41$
$
\Rightarrow n=\frac{-41}{3}
$
Which is not possible being negative.
$
\therefore n=14
$
Now, $x = a +( n -1) d$
$
\begin{aligned}
& =1+(14-1) \times 3 \\
& =1+13 \times 3 \\
& =1+39 \\
& =40 \\
& \therefore x=40 .
\end{aligned}
$

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