NTSE Stage 2 SAT 2016 Question Paper

Question : 46 of 100

Marks: +1, -0

\S_1 , \S_2 , \S_3 , ......., \S_\r

are the sum of first n terms of r arithmetic progression whose first terms are 1, 2, 3, ......... and whose common differences are 1, 3, 5, ........ respectively, then the value of

\S_1 + \S_2 + \S_3 + ......\S_\r

${(\nr-1)(\nr+1)}/2$
${(\nr+1)\nr}/2$
${(\nr-1)\nr}/2$
${\n(\nr+1)}/2$

Validate

Solution:

\S_1=\n/2[2(1)+(\n-1)(1)]

\S_2=\n/2[2(2)+(\n-1)(3)]

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.
.

\S_\r=\n/2[2(\r)+(\n-1)(2\r-1)]

(+) (+)

\S_1+\S_2+......+\S_\r=\n/2

[(2){\r(\r+1)}/2+(\n+1)\r/2[1+2\r-1]]

=\n/2[\r(\r+1)+(\n-1)\r^2]

=\nr/2[\r+1+\nr-\r]

=\nr/2[\nr+1]

So the value of

\S_1 , \S_2 , \S_3 , ......., \S_\r

\nr/2[\nr+1]

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