The sum of the series $3.6 + 4.7 + 5.8 + . . . . .$ upto $(n - 2)$ terms is

n^{3} + n^{2} + n + 2

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\frac{1}{6} (2 n^{3} + 12 n^{2} + 10 n - 84)

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n^{3} + n^{2} + n

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None of these

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Solution

The correct option is D None of these
We can see that this is an Arithmatic Progression
$a =$ first term $= 3.6$
$d =$ common difference $= 1.1$
$m = (n - 2) =$ number of terms
$∴$ Sum, $s = \frac{m}{2} (2 a + (m - 1) d)$
$= \frac{n - 2}{2} (2 (3.6) + (n - 3) (1.1)$
$= \frac{n - 2}{2} (7.2 + (1.1) n - 3.3)$
$= \frac{n - 2}{2} (3.9 + 1.1 n)$
$\frac{(n - 2) (39 + 11 n)}{20}$
$∴$ The correct option is $D$ = None of these

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