JEE Main 2022 · 27 Jul · Shift 1 · Mathematics Q6

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MathematicsSingle correct+4 / -1Question 6 of 90

Suppose $a_1,a_2,\ldots,a_n,\ldots$ be an arithmetic progression of natural numbers. If the ratio of the sum of first five terms to the sum of first nine terms of the progression is 5 : 17 and $110<a_{15}<120$ , then the sum of the first ten terms of the progression is equal to

290

380

460

510

Answer and worked solution

Official answer: B

Ratio. $\frac{5(a+2d)}{9(a+4d)}=\frac5{17}$ gives $d=4a$ .

$a_{15}$ $=a+14d=57a\in(110,120)$ , so $a=2$ , $d=8$ .

$S_{10}$ $=5(4+72)=380$ . (B)

Topics:Arithmetic progression

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JEE Main 2022 · 27 Jul · Shift 1, Mathematics question 6