# The sum of the series  $1+2\times3+3\times 5+4\times7+.......upto\:\:\:11^{th}$ term is : Option 1) $915$ Option 2) $946$ Option 3) $945$ Option 4) $916$

$\\1+2\times3+3\times5+4\times7 upto\:\:\:11^{th }\:\:term\\\\\\\:$

$\\\sum_{r=1}^{11}r(2r-1)=\sum_{r=1}^{11}2r^{2}-r\\\\\\\:=2\frac{n(n+1)(2n+1)}{6}-\frac{n(n+1)}{2}\\\\\\\:=2\frac{11\times12\times23}{6}-\frac{11\times126}{2}\\\\\\\:=4\times11\times23-66\\\\\\\:=253\times4-61\\\\\\\:=1012-66\\\\\\\:=946$

Option 1)

$915$

Option 2)

$946$

Option 3)

$945$

Option 4)

$916$

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