# How do you find the sum of the first 25 terms of the sequence: 7,19,31,43...?

$3775$

#### Explanation:

The given series:

$7 , 19 , 31 , 43 , \setminus \ldots$

Above series is an arithmetic progression with a common difference

$d = 19 - 7 = 31 - 19 = 43 - 31 = \setminus \ldots = 12$

First term: $a = 7$

The sum of first $n$ terms of an AP with term $a$ & a common difference $d$ is given as

${S}_{n} = \frac{n}{2} \left(2 a + \left(n - 1\right) d\right)$

Hence, the sum of first $n = 25$ terms of an AP with term $a = 7$ & a common difference $d = 12$ is given as

${S}_{25} = \frac{25}{2} \left(2 \setminus \cdot 7 + \left(25 - 1\right) 12\right)$

$= 3775$