Question

The value obtained by subtracting the ${10}^{th}$ term of an AP from the ${17}^{th}$ term is $56$. Find the common difference.

• A. $7$
• B. $16$
• C. $9$
• D. $8$

Answer 1

The correct option is D $8$

In an Arithmetic Progression the general term of an A.P. is given by $T_n$:

$T_n=a+(n-1)d$

According to the statement:

$T_{17}-T_{10}=56$

$a+(17-1)d-[a+(10-1\left)d\right]=56$

$a+16d-[a+9d]=56$

$a+16d-a-9d=56$

$7a=56$

$d=8$