Question

If the $7^{th}$ and ${13}^{th}$ term an Arithmetic progression are $34$ and $64$ respectively. then the common difference is,

• A. $5$
• B. $10$
• C. $17$
• D. $32$

Answer 1

The correct option is A $5$

We know $a_n=a+(n-1)d$

So, $a_7=a+6d=\mathrm{34.............}\left(1\right)a_{13}=a+12d=\mathrm{64.............}\left(2\right)$

Subtracting (1) from (2)

$6d=30\Rightarrow d=5$