# The geometric progression is given by the condition bn = -104 * 3 ^ n. Find the sum of its first 4 terms.

September 28, 2021 | education

| Let us find successively the first four terms of a given geometric progression, and then we find the sum of these terms.

Substituting the values n = 1, n = 2, n = 3 and n = 4 into the formula for the nth term bn = -104 * 3 ^ n of this progression, we get:

b1 = -104 * 3 ^ 1 = -104 * 3;

b2 = -104 * 3 ^ 2 = -104 * 9;

b3 = -104 * 3 ^ 3 = -104 * 27;

b4 = -104 * 3 ^ 4 = -104 * 81.

We find the sum of the first four members of this geometric progression:

b1 + b2 + b3 + b4 = -104 * 3 – 104 * 9 – 104 * 27 – 104 * 81 = -104 * (3 + 9 + 27 + 81) =

-104 * ((3 + 27) + (81 + 9)) = -104 * (30 + 90) = -104 * 120 = -12480.

Answer: the sum of the first four members of this progression is -12480.

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