Find the sum of the first 24 terms of the lis | vedclass

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(C) The $n^{th}$ term is given by $a_{n} = 3 + 2n$.To find the terms of the sequence,substitute $n = 1, 2, 3, \dots$:$a_{1} = 3 + 2(1) = 5$$a_{2} = 3

Vedclass · Accepted Answer

$672$

Vedclass · Answer

(C) The $n^{th}$ term is given by $a_{n} = 3 + 2n$.To find the terms of the sequence,substitute $n = 1, 2, 3, \dots$:$a_{1} = 3 + 2(1) = 5$$a_{2} = 3 + 2(2) = 7$$a_{3} = 3 + 2(3) = 9$The sequence is $5, 7, 9, 11, \dots$Since the difference between consecutive terms is constant $(7 - 5 = 2, 9 - 7 = 2)$,this is an Arithmetic Progression $(AP)$ with first term $a = 5$ and common difference $d = 2$.The sum of the first $n$ terms of an $AP$ is given by $S_{n} = \frac{n}{2}[2a + (n - 1)d]$.For $n = 24$:$S_{24} = \frac{24}{2}[2(5) + (24 - 1)2]$$S_{24} = 12[10 + (23 	imes 2)]$$S_{24} = 12[10 + 46]$$S_{24} = 12 	imes 56 = 672$.Thus,the sum of the first $24$ terms is $672$.

Find the sum of the first $24$ terms of the list of numbers whose $n^{th}$ term is given by $a_{n} = 3 + 2n$.

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