Find the sum of all negative members of the arithmetic progression – 6.8; – 6.6; …

1. An arithmetic progression A (n) is given:

A1 = -6.8;

A2 = -6.6;

2. Difference progression:

d = A2 – A1 = (-6.6) – (-6.8) = 0.2;

3. Find the number of the member of the progression:

An = A1 + d * (n -1) = 0;

d * (n – 1) = -A1 = 6.8;

n – 1 = 6.8 / 0.2 = 34;

n = 34 +1 = 35;

4. The last negative term of the progression:

A (n -1) = A (35 -1) = A34 = A35 – d = 0 – 0.2 = -0.2;

5. The sum of all negative members of the progression:

S34 = ((A1 + A34) / 2) * 34 = ((-6.8) + (-0.2)) * 17 = (-7) * 17 = -119;

5. You can check:

S35 = S34 = (A1 + A35) / 2 * 35 = A1 / 2 * 35 = (-6.8) * 17.5 = -119.

Answer: the sum of all negative members of the progression is -119.