Find the sum of the series: 3 + 7 + 11 + ldot | vedclass

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Question

(D) The given series is an Arithmetic Progression $(AP)$ where the first term $a = 3$ and the common difference $d = 7 - 3 = 4$.The last term $l$ (or

Vedclass · Accepted Answer

$1830$

Vedclass · Answer

(D) The given series is an Arithmetic Progression $(AP)$ where the first term $a = 3$ and the common difference $d = 7 - 3 = 4$.The last term $l$ (or $a_n$) is $119$.The formula for the $n^{th}$ term of an $AP$ is $a_n = a + (n - 1)d$.Substituting the values: $119 = 3 + (n - 1)4$.$116 = (n - 1)4$.$n - 1 = 29$,so $n = 30$.The sum of $n$ terms of an $AP$ is given by $S_n = \frac{n}{2}(a + l)$.$S_{30} = \frac{30}{2}(3 + 119) = 15 	imes 122 = 1830$.

Find the sum of the series: $3 + 7 + 11 + \ldots + 119$.

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