Question

In an A.P . the ${10}^{th}$ term is 46, sum of the $5^{th}$ and $7^{th}$ term is 52. Find the A.P .

Answer 1

Given: ${10}^{th}$ term$=46$

$\Rightarrow a+9d=46$ .........$\left(1\right)$

Sum of $5^{th}$ term$+7^{th}$ term$=52$

$\Rightarrow a+4d+a+6d=52$

$\Rightarrow 2a+10d=52$

$\Rightarrow a+5d=26$ .........$\left(2\right)$

Eqn$\left(2\right)-$Eqn$\left(1\right)$ we get

$a+5d-a-9d=26-46$

$\Rightarrow -4d=-20$

$\therefore d=\frac{-20}{-4}=5$

substituting $d=5$ in $\left(1\right)$ we get

$a+9\times 5=46$

$\Rightarrow a=46-45=1$

$\therefore a=1,d=5$

The A.P is $a,a+d,a+2d,a+3d,..,a+(n-1)d$

$1,1+5,1+2\times 5,1+3\times 5,...,1+(n-1)5$

or $1,6,11,16,...,5n-4$