Question

If the $6^{th}$ and ${15}^{th}$ term of an AP are $29$ and $74$ respectively, then the ${31}^{st}$ term is

• A. $145$
• B. $149$
• C. $159$
• D. $154$

Answer 1

The correct option is D $154$

$a_{15}=a+14d=74$ ,,,,,(1)
$a_6=a+5d=29$ .....(2)
Subtract (1) by $2$
$\Rightarrow -9d=-45$
$\Rightarrow d=5$
Substitute the value of $d$ in (1)
$\Rightarrow 74=a+5\times 14$
$\Rightarrow a=4$
Then $a_{31}=a+30d$
$\Rightarrow 4+30\times 5=154$
Hence, ${31}^{st}$ term is $154$.