The sum of five members of the arithmetic progression is 60, and the difference between

| May 22, 2021 | education

The sum of five members of the arithmetic progression is 60, and the difference between the fourth and the second is 8. Find the fifth term of the progression.

Since the difference between the fourth and second members of the progression is 8, it means that the difference between adjacent members of the progression will be equal to:

8/2 = 4.

We draw up an equation in which the first term of the arithmetic progression is written as x.

In this case, the second term will be equal to: x + 4, the third – x + 4 + 4 = x + 8.

The fourth will be: x + 8 + 4 = x + 12.

Fifth – x + 12 + 4 = x + 16.

Let’s get the equation of the sum.

x + x + 4 + x + 8 + x + 12 + x + 16 = 60.

5 * x = 60 – 40.

5 * x = 20.

x = 20/5 = 4 (the first term of the progression).

x + 16 = 4 + 16 = 20 (the fifth term of the progression).

Answer: 20.



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