JEE Main 2014 · 9 Apr · Shift 1 · Mathematics Q69

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MathematicsSingle correct+4 / -1Question 69 of 90

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 $^{\text{th}}$ term is :

Answer and worked solution

Official answer: C

$a+d=12$ and $S_9=9(a+4d)=9(12+3d)$ , with $200<S_9<220$ :
$22.2<12+3d<24.4\implies d=4\ (\text{integer}),\quad a=8.$
$T_4=a+3d=20$ .

Topics:Arithmetic progression

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JEE Main 2014 · 9 Apr · Shift 1, Mathematics question 69