Find the sum of 24 terms of the list of numbers whose n$^{th}$ term is given by:

$a_n = 3 + 2n$

The formula for the n$^{th}$ term is $a_n = 3 + 2n$.

The sum of the first 24 terms is needed.

---

For the first term (n = 1):

$a_1 = 3 + 2(1)$

$a_1 = 5$

For the last term (n = 24):

$a_{24} = 3 + 2(24)$

$a_{24} = 3 + 48$

$a_{24} = 51$

---

Checking the pattern:

$a_1 = 5$

$a_2 = 3 + 2(2) = 7$

$a_3 = 3 + 2(3) = 9$

The difference between consecutive terms is always 2, so this is an arithmetic progression.

---

For an arithmetic progression, the sum of n terms is:

$S_n = \frac{n}{2} \times (\text{First term} + \text{Last term})$

$S_{24} = \frac{24}{2} \times (5 + 51)$

$S_{24} = 12 \times 56$

$S_{24} = 672$

Therefore, the sum of 24 terms is 672.