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solivagantjn3010
27.06.2019 •
Mathematics
Write an explicit rule and recursive rule for a geometric sequence with a second term of 6 and a third term of 12.
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Ответ:
Step-by-step
Given:
Geometric sequence with
second term, T2 = 6
third term, T3 = 12
Wants to have the explicit and recursive rules.
Solution:
common ratio, r = 12/6 = 2
Therefore the first term, T1
= second term /r
= 6/2
=3
Thus the absolute rule is
Tn = T1 *r^(n-1) where T1 = 3, r=2. Check: T3 = T1*2^(3-1) = 3*2^2=12 ...good
The recursive rule (depending on the previous term)
Tn = Tn-1*r = 2*Tn-1
Ответ: