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8. sequence and series — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS8. sequence and series1 Mark
MCQ
The sum to $20$ terms of the series $2.2^2-3^2+2.4^2-5^2+2.6^2-\ldots \ldots$ is equal to $........$.
  • A
    $1311$
  • B
    $1312$
  • ✓
    $1310$
  • D
    $1313$
✓

Answer

Correct option: C.
$1310$
c
$\left(2^2-3^2+4^2-5^2+20 \text { terms }\right)+ \left(2^2+4^2+\ldots .+10 \text { terms }\right)$

$-(2+3+4+5+\ldots . .+11)+4\left[1+2^2+\ldots \ldots .10^2\right]$

$-\left[\frac{21 \times 22}{2}-1\right]+4 \times \frac{10 \times 11 \times 21}{6}$

$=1-231+14 \times 11 \times 10$

$=1540+1-231$

$=1310$

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