The first few members of the arithmetic progression are written out: -7, -4, -1

| August 2, 2021 | education

The first few members of the arithmetic progression are written out: -7, -4, -1 Find the sum of the first 6 of its members.

According to the condition of the problem, the first three terms of the arithmetic progression аn are given: а1 = -7, а2 = -4, а3 = -1.

Using the definition of an arithmetic progression, we find the difference d of this progression:

d = a2 – a1 = -4 – (-7) = -4 + 7 = 3.

Using the formula for the sum of the first n members of the arithmetic progression Sn = (2 * a1 + d * (n – 1)) * n / 2 for n = 6, we find the sum of the first 6 members of this arithmetic progression:

S6 = (2 * a1 + d * (6 – 1)) * 6/2 = (2 * a1 + d * 5) * 3 = (2 * (-7) + 3 * 5) * 3 = (-14 + 15) * 3 = 1 * 3 = 3.

Answer: the sum of the first 6 members of this arithmetic progression is 3.



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