Question

In an A.P. 17^th term is 7 more than its 10^th term. Find the common difference.

Answer 1

It is given that,
a₁₇ = 7 + a₁₀

We know that,
$$\begin{gathered} a_n=a+\left(n-1\right)d \\ {a}_{17}=7+a_{10} \\ \Rightarrow a+\left(17-1\right)d=7+a+\left(10-1\right)d \\ \Rightarrow a+16d=7+a+9d \\ \Rightarrow 16d=7+9d \\ \Rightarrow 16d-9d=7 \\ \Rightarrow 7d=7 \\ \Rightarrow d=1 \end{gathered}$$

Hence, the common difference is 1.