# The sum of the first five terms of the arithmetic progression is 39, and the second term is 5.

August 29, 2021 | education

| **The sum of the first five terms of the arithmetic progression is 39, and the second term is 5. Find the sum of the first eight terms.**

1. An arithmetic progression A (n) is set, for whose members the parameters are set:

S5 = 39;

A2 = 5;

2. Let’s try to determine its main parameters: A1 and d;

A2 = A1 + d;

A1 = A2 – d = 5 – d;

3. The sum of the five members of the progression:

S5 = (2 * A1 + d * (5 – 1)) * 5/2 =

5 * A1 + d * 10 = 5 * (5 – d) + 10 * d =

25 + 5 * d = 39;

5 * d = 39 – 25 = 14;

d = 14/5 = 2.8;

A1 = 5 – d = 5 – 2.8 = 2.2;

4. Now let’s calculate the sum of the first eight terms of the progression A (n):

S8 = (2 * A1 + d * (8 – 1)) * 8/2 =

(2 * 2.2 + 2.8 * 7) * 4;

(4.4 + 19.6) * 4 = 96.

Answer: sum S8 = 96.

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