Find the sum of the first fourteen terms of the arithmetic progression 30; 28; 26; …

The arithmetic progression (an) is given by its first three terms a1 = 30; a2 = 28; a3 = 26.

In order to find the sum of the first fourteen members of an arithmetic progression, we need to find the difference of the arithmetic progression and recall the formula for finding the sum of the first n terms of an arithmetic progression through the difference and the first term of the progression:

We look for the difference in the progression using the formula:

d = an + 1 – an;

d = a2 – a1 = 28 – 30 = -2;

We look for the sum of the first 14 members of the progression using the formula:

Sn = (2a1 + d (n – 1)) / 2 * n;

S14 = (2 * 30 – 2 (14 – 1)) / 2 * 14 = (60 – 2 * 14) / 2 * 14 = (60 – 28) / 2 * 14 = 16 * 14 = 224.