Question

Which term of the A.P $3,10,17,.......$ will be $84$ more than its ${13}^{th}$ term?

• A. ${23}^{rd}$
• B. ${25}^{th}$
• C. ${27}^{th}$
• D. ${28}^{th}$

Answer 1

The correct option is B ${25}^{th}$

Given A.P is $1,10,\mathrm{17.....}$
${13}^{th}$ term $a_{13}=a+12d$
$\Rightarrow 3+12\times 7$
$\Rightarrow 87$
According to the question
$a_n=a_{13}+84$
$\Rightarrow 87+84$
$\Rightarrow 171$
$\therefore a_n=a+(n-1)d$
$171=3+(n-1)7$
$171=3+7n-7$
$7n=175$
$\therefore n=25$
Hence ${25}^{th}$ term is $84$ more than ${13}^{th}$ term.