Question

If the common difference of an AP is $5,$ then what is $a_{18}-a_{13}$ ?

• A. $5$
• B. $20$
• C. $25$
• D. $30$

Answer 1

Answer: (C)

$25$

Hint: $n^{th}$ term of an A.P. is $a_n=a+(n-1)d$ where $a$ is first term and $d$ is common difference.

Given:
value of common difference $,d=5$
Step 1 : Find the value of ${18}^{th}$ term i.e, $a_{18}$ by replacing $n$ with $18$ in the $n^{th}$ term of the A.P
$\Rightarrow a_n=a+(n-1)d$
$\Rightarrow a_{18}=a+(18-1)d$

$\therefore a_{18}=a+17d$
Step 2 : Find the value of ${13}^{th}$ term i.e, $a_{13}$ by replacing $n$ with $13$ in the $n^{th}$ term of the A.P

$\Rightarrow a_n=a+(n-1)d$

$\Rightarrow a_{13}=a+(13-1)d$

$\therefore a_{13}=a+12d$
Step 3 : Find the difference between $a_{18}$ and $a_{13}$
$a_{18}-a_{13}$
$=[a+17d]-[a+12d]$
$=a+17d-a-12d$
$=5d=5\times 5=25$
Final step : Hence, $a_{18}-a_{13}=25$