The fifth term of the geometric progression is 12, and the seventh is 27. Find the sixth term of this progression.
| August 4, 2021 | education
One of the main formulas for a geometric progression:
b (n + 1) = bn * q.
Substitute the given values:
b6 = b5 * q = 12q;
b7 = b6 * q = 12q * q = 12q ^ 2.
27 = 12q ^ 2;
q ^ 2 = 27/12 = 9/4;
q = -3/2 and 3/2.
Then b6 = 12 * q = -18 or 18.
Answer: b6 = -18, b6 = 18.
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