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

The 1st term is:

$a_1=3+2(1)$

$a_1=3+2$

$a_1=5$

The Second term:

$a_2=3+2(2)$

$= 3+4$

$a_2=7$

The third term:

$a_3=3+2(3)$

$a_3=3+6$

$a_3=9$

The Fourth term:

$a_4=3+2(4)$

$=3+8$

$a_4=11$

Therefore the series is $5,7,9,11,...$

There is a constant difference of $2$ hence it is an Arithmetic Progression.

To calculate the sum of the first 24 terms, use the formula:

$$S_n =\dfrac{n}{2}[2a+(n-1)d]$$

Substituting, $n=24, a=5$

Thus the sum is $672$
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