IIT-JEE 2007 · Paper 1 · Mathematics Q60

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Paragraph for Question Nos. 58 to 60

Let $V_r$ denote the sum of the first $r$ terms of an arithmetic progression (A.P.) whose first term is $r$ and the common difference is $(2r-1)$ . Let
$T_r=V_{r+1}-V_r-2\quad\text{and}\quad Q_r=T_{r+1}-T_r\quad\text{for }r=1,2,\ldots$

Which one of the following is a correct statement?

Q_1,Q_2,Q_3,\ldots

are in A.P. with common difference 5

Q_1,Q_2,Q_3,\ldots

are in A.P. with common difference 6

Q_1,Q_2,Q_3,\ldots

are in A.P. with common difference 11

Q_1=Q_2=Q_3=\cdots

Answer and worked solution

Official answer: B

Difference of $T$ . $Q_r=T_{r+1}-T_r=3\left[(r+1)^2-r^2\right]+2=6r+5$ .

So $Q_1,Q_2,\ldots=11,17,23,\ldots$ , an A.P. with common difference 6.

(B)

Topics:Arithmetic progression

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IIT-JEE 2007 · Paper 1, Mathematics question 60