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aaron2113
02.03.2020 •
Mathematics
This recursive formula represents a geometric sequence: a1 = 2 an = 6(an − 1); for n ≥ 2 Select the geometric sequence that can be constructed from the given recursive formula, and select the explicit formula for the sequence.
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Ответ:
f(n)=2X6ⁿ⁻¹
Step-by-step explanation:
a₁=2
aₙ=6aₙ₋₁ for n≥2
a₂=6a₂₋₁=6a₁=6*2=12
a₃=6a₃₋₁=6a₂=6*12=72
a₄=6a₄₋₁=6a₃=6*72=432
This is a geometric sequence with:
First term, a=2
Common ratio, r= 12/2=6
For a geometric sequence, the nth term is given by:
Uₙ=arⁿ⁻¹
Uₙ=2X6ⁿ⁻¹
Therefore, the explicit formula for the sequence f(n) is given as:
f(n)=2X6ⁿ⁻¹
Ответ:
x=-6/4 or -1![\frac{1}{2}](/tpl/images/0346/2463/9cdae.png)
Step-by-step explanation: