Identify parameters

Identify the values provided for the arithmetic progression: the first term $a = 5$, common difference $d = 2$, and number of terms $n = 10$.

$a=5, d=2, n=10$

Apply sum formula

Substitute the given values into the formula for the sum of $n$ terms of an AP: $S_n = \frac{n}{2} [2a + (n - 1)d]$.

$S_{10} = \frac{10}{2} [2(5) + (10^{-1})2]$

Calculate the result

Perform the arithmetic operations inside the brackets: $10 + (9 \times 2) = 10 + 18 = 28$. Then multiply by $\frac{10}{2} = 5$.

$S_{10} = 5 \times [10 + 18] = 5 \times 28 = 140$