7+12+17+ldots+102 = ldots | vedclass

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Question

(C) The given series is $7, 12, 17, \ldots, 102$.This is an Arithmetic Progression $(AP)$ where the first term $a = 7$ and the common difference $d =

Vedclass · Accepted Answer

$1090$

Vedclass · Answer

(C) The given series is $7, 12, 17, \ldots, 102$.This is an Arithmetic Progression $(AP)$ where the first term $a = 7$ and the common difference $d = 12 - 7 = 5$.The last term $l = a_n = 102$.The formula for the $n^{th}$ term is $a_n = a + (n - 1)d$.Substituting the values: $102 = 7 + (n - 1)5$.$102 - 7 = (n - 1)5 \implies 95 = (n - 1)5$.$n - 1 = 19 \implies n = 20$.The sum of $n$ terms of an $AP$ is given by $S_n = \frac{n}{2}(a + l)$.$S_{20} = \frac{20}{2}(7 + 102) = 10 	imes 109 = 1090$.

$7+12+17+\ldots+102 = \ldots$

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