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 4th term is :

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 4th term is : (A) 8 (B) 16 (C) 20 (D) 24

Tardigrade Admin · Accepted Answer

(12 - d) + 12 + (12 + d) + (12 + 2d) +.... 12 +7d =12 Ã 9 + 27d = 108 + 27d now according to question 200 < 108 + 27d < 220 92 < 27d < 112 (92/27) < d < (112/27) ⇒ d = 4 only integer ⇒ 4th term = 12 + 2d = 12 + 8 = 20

Q. 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 $4^{t h}$ term is :

8

16

20

24

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

Q. 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 4th term is :

8

16

20

24

(12−d)+12+(12+d)+(12+2d)+....12+7d =12×9+27d=108+27d now according to question 200<108+27d<220 92<27d<112 2792​<d<27112​ ⇒d=4 only integer ⇒4th term = 12+2d=12+8=20

Q. 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 $4^{t h}$ term is :

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