Find the sum of the series: 7 + 10 frac{1}{2} | vedclass

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Question

(C) The given series is $7, 10.5, 14, \ldots, 84$. This is an Arithmetic Progression $(AP)$ where the first term $a = 7$ and the common difference $d

Vedclass · Accepted Answer

$1046 \frac{1}{2}$

Vedclass · Answer

(C) The given series is $7, 10.5, 14, \ldots, 84$. This is an Arithmetic Progression $(AP)$ where the first term $a = 7$ and the common difference $d = 10.5 - 7 = 3.5 = \frac{7}{2}$. Let the number of terms be $n$. The $n^{th}$ term is given by $a_n = a + (n - 1)d$. Substituting the values: $84 = 7 + (n - 1) 	imes \frac{7}{2}$. $84 - 7 = (n - 1) 	imes \frac{7}{2} \implies 77 = (n - 1) 	imes \frac{7}{2}$. $(n - 1) = 77 	imes \frac{2}{7} = 11 	imes 2 = 22$. $n = 22 + 1 = 23$. The sum of $n$ terms of an $AP$ is $S_n = \frac{n}{2} (a + a_n)$. $S_{23} = \frac{23}{2} (7 + 84) = \frac{23}{2} 	imes 91 = \frac{2093}{2} = 1046.5 = 1046 \frac{1}{2}$.

Find the sum of the series: $7 + 10 \frac{1}{2} + 14 + \ldots + 84$.

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