Question

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

• A. ${25}^{th}$
• B. ${24}^{th}$
• C. ${35}^{th}$
• D. ${34}^{th}$

Answer 1

Answer: (A)

${25}^{th}$

Clearly, the given sequence is an AP with first term $a=3$ and common difference $d=10-3=7$.
Given $n^{th}$ term is $84$ more than its ${13}^{th}$ term.
$\Rightarrow t_n=t_{13}+84$
$\Rightarrow a+(n-1)d=(a+12d)+84$
$\Rightarrow (n-1)d=12d+84$
$\Rightarrow (n-1)7=12\times 7+84$
$\Rightarrow (n-1)7=7(12+12)$
$\Rightarrow n-1=24$
$\Rightarrow n=25$
Therefore ${25}^{th}$ term is the required term.