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

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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