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Answer :
Final answer:
The 12th term of the geometric sequence -7x⁴, -7x⁵, -7x⁶, is -7x¹⁵, which is found using the formula for the nth term of a geometric sequence.
Explanation:
To find the 12th term of the given geometric sequence -7x⁴, -7x⁵, -7x⁶, we first identify the first term (a) and the common ratio (r) of the sequence. The first term a is -7x⁴. By observing the sequence, we can determine that to get from one term to the next, we multiply by x, so the common ratio r is x.
The nth term of a geometric sequence is given by the formula a * rⁿ⁻¹. To find the 12th term, we substitute 12 for n, -7x⁴ for a, and x for r:
a * rⁿ⁻¹ = (-7x⁴) * x¹²⁻¹ = (-7x⁴) * x¹¹ = -7x⁴⁺¹¹ = -7x¹⁵.
So, the 12th term of the geometric sequence is -7x¹⁵.
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