Question

Find $a_{30}-a_{20}$ for the $AP$ $:a,a+d,a+2d,a+3d,...$

• A. $60d$
  
• B. $50d$
• C. $10d$
  
• D. $\frac{3}{2}d$

Answer 1

Answer: (C)

$10d$

Here the first term is $a$ and the common difference is $d$.
$n^{th}$ term of the AP is given by,

$a_n=a+(n-1)d$
$\therefore a_{20}=a+19d$ ...$\left(1\right)$
$a_{30}=a+29d$ ...$\left(2\right)$
On subtracting $\left(1\right)$ from $\left(2\right)$, we get
$a_{30}-a_{20}=10d$