Question

Solve the solution: $1+4+7+10..........................+x=287$

Answer 1

Given, $1+4+7+10..........................+x=287$

We need to find the value of $x$,

First-term, $a=1$

Common difference, $d=4-1=3$

$S_n=287$

Using the formula,$S_n=\frac{n}{2}(2a+(n-1\left)d\right)$

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

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

$574=n(3n-1)$

$574=3n^2-n$

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

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

$3n(n-14)+41(n-14)=0$

$(3n+41)(n-14)=0$

$$\begin{gathered} (3n+41)=0or\left(n-14\right)=0 \\ n=\frac{-41}{3}orn=14 \end{gathered}$$

As number of terms cannot be negative so $n=14$.

Thus, $x$ is the $14th$ term,

Using formula,$a+(n-1)d=x$

$$\begin{gathered} x=1+\left(14-1\right)3 \\ x=1+13\times 3 \\ x=1+39 \\ x=40 \end{gathered}$$