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Sequences and Series — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsSequences and Series1 Mark
MCQ
Find the sum of series $6^2+ 7^2+…………………..+ 15^2$.
  • A
    $55$
  • ✓
    $1185$
  • C
    $1240$
  • D
    $1385$
✓

Answer

Correct option: B.
$1185$
$6^2+7^2+\ldots \ldots \ldots \ldots \ldots \ldots+15^2 $
$=\left(1^2+2^2+3^2+\ldots \ldots \ldots+15^2\right)-\left(1^2+2^2+3^2+4^2+5^2\right) $
$=\frac{15\times16\times31}{6}-\frac{5\times6\times11}{6}$
$=1240-55$
$=1185.$

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