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  • Find the sum of first 17 terms of an AP whose 4th and 9th terms are -15 and -30 respectively.

Find the sum of first 17 terms of an AP whose 4th and 9th terms are -15 and -30 respectively.

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a_{4} = -15, a_{9} = -30 \\ a_{4} = -15 \quad a_{9} = -30 \\ a + 3d = -15 \quad \ldots (1) \\ a + 8d = -30 \quad \ldots (2) \quad (\text{Using } a_{n} = a + (n - 1)d) \\ \text{from equation (1) and (2)}

\\-5d = 15\\ d = - 3\\ $ Put d = - 3 in (1)\\$ a + 3(-3) = - 15\\ a = - 15 + 9\\ a = - 6\\ {{S}_{17}}=\frac{17}{2}\left[ 2\left( -6 \right)+\left( 17-1 \right)\left( -3 \right) \right] \\Using \ {{S}_{n}}=\frac{n}{2}\left[ 2a+\left( n-1 \right)d \right] \\ \begin{aligned} & =\frac{17}{2}\left[ -12-48 \right] \ & =\frac{17}{2}\left[ -60 \right] \ \end{aligned} \\ S\textsubscript{17} = - 510\\

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