Question

The sum of $5th$and $7th$ terms of an A.P. is$52$ and the $10th$term is $46$. Find the A.P..

Answer 1

Given, sum of the 5th and 7th term is $52$.

$\therefore a+4d+a+6d=52\Rightarrow 2a+10d=52⟶\left(1\right)$

And, the 10th term is $46$.

$\therefore a+9d=46$

multiplying it by 2 we get,

$2a+18d=92⟶\left(2\right)$

Solving equations $\left(1\right)$ and $\left(2\right)$ we get,

$8d=40\Rightarrow d=5$

Substituting the value of d in $\left(1\right)$ we get,

$2a+(10\times 5)=52\Rightarrow 2a=52-50\Rightarrow a=1$

Therefore, the required $A.P.$ is,

$1,6,11,16,21,26,31,.....$