Question

Is $68$ a term of the A.P. $7,10,13,.....$?

Answer 1

Given sequence is $7,10,13,...$

The first term $a=7$ and

the common difference $d=10-7=3$

Let the $n^{th}$ term be $68$

We know that the $n^{th}$ term of the arithmetic progression is given by $a+(n-1)d$

Therefore, $a+(n-1)d=68$

$⟹7+(n-1)\ast \left(3\right)=68$

$⟹7-3+3n=68$

$⟹4+3n=68$

$⟹3n=68-4$

$⟹n=\frac{64}{3}$

$n$ cannot be a fraction. Therefore, $68$ is not the term of the given A.P.