Find the sum of the first eighteen members of the arithmetic progression: 5; 2; -1; -4; …

Let an arithmetic progression be given a (1) = 5, a (2) = 2, a (3) = -1, a (4) = -4, …. Denote by d the difference of the progression.

d = a (2) – a (1) = 2 – 5 = -3.

Let’s find the eighteenth term according to the general formula:

a (n) = a (1) + (n – 1) d;

a (18) = 5 + 17 (-3) = 5 – 51 = -46.

Now let’s find the sum of 18 members:

S (n) = (a (1) + a (n)) / 2 n;

S (18) = (a (1) + a (18)) / 2 18 = (5 – 46) / 2 18 = -369.