Question

Given an $A.P$. whose terms 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 $4^{th}$ term is :

• A. 8
• B. 16
• C. 20
• D. 24

Answer 1

Answer: (C)

20

Answer 2

$\left(12 - d\right) + 12 + \left(12 + d\right) + \left(12 + 2d\right) +.... 12 +7d$
$=12 ? 9 + 27d = 108 + 27d$
now according to question
$200 < 108 + 27d < 220$
$92 < 27d < 112$
$\frac{92}{27} < d < \frac{112}{27}$
$\Rightarrow d = 4$ only integer
$\Rightarrow 4$th term = $12 + 2d = 12 + 8 = 20$