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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