Question

Given an A.P. whose term are all positive integers. The sum of its first nine terms is greater than $200$ and less than $220$. If the second term in it is $12$, then its $4^{th}$ terms is

• A. 24
• B. 8
• C. 16
• D. 20

Answer 1

The correct option is D 20

$7_2=a+d=12$

$\Rightarrow a=12-d$

$200<S_9<220$

$200<\frac{9}{2}[2a+8d]<220$

$\frac{400}{9}<2(a+4d)<\frac{440}{9}$

$\frac{200}{9}<12-d+4d<\frac{220}{9}$

$\frac{200}{9}<12+3d<\frac{220}{9}$

$\frac{200}{27}<4+d<\frac{220}{27}$

$\frac{92}{27}<d<\frac{112}{27}$

$3.4<d<4.14$

So $d=4$, $a=8$

$7_4=a+3d$

$=8+12=20$.