$a_{1} = 1.5, a_{20} = 58.5$ in an arithmetic series, find $S_{15}$ .

137.5

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237.5

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337.5

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437.5

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Solution

The correct option is D $337.5$
$a_{n} = a + (n - 1) d$
$\Rightarrow a_{20} = 1.5 + (20 - 1) d$
$\Rightarrow 58.5 - 1.5 = 19 d$
$\Rightarrow 57 = 19 d$
$\Rightarrow d = 3$
$S_{n} = \frac{n}{2} [2 a + (n - 1) d]$
$\Rightarrow S_{15} = \frac{15}{2} [2 \times 1.5 + (15 - 1) 3]$
$\Rightarrow S_{15} = 7.5 [3 + 42]$
$\Rightarrow S_{15} = 7.5 [45]$
$\Rightarrow S_{15} = 337.5$

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a1=1.5,a20=58.5 in an arithmetic series, find S15.

The correct option is D 337.5an=a+(n−1)d⇒a20=1.5+(20−1)d⇒58.5−1.5=19d⇒57=19d⇒d=3Sn=n2[2a+(n−1)d]⇒S15=152[2×1.5+(15−1)3]⇒S15=7.5[3+42]⇒S15=7.5[45]⇒S15=337.5

$a_{1} = 1.5, a_{20} = 58.5$ in an arithmetic series, find $S_{15}$ .