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vitfil [10]
3 years ago
12

Explain why the exponents cannot be added in the product 12^3 and 11^3

Mathematics
1 answer:
GrogVix [38]3 years ago
4 0
Because bases are different.

a^n · a^m = a^(n+m)
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Complete the recursive formula of the geometric sequence 16\,,\,3.2\,,\,0.64\,,\,0.128,...16,3.2,0.64,0.128,
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Answer:

a_{n+1}=0.2a_n for all n>0, a_1=16

Step-by-step explanation:

Let \{a_n\}=\{16,3.2,0.64,0.128,\cdots \} be the sequence described.

A geometric sequence has the following property: there exists some r (the ratio of the sequence) such that \frac{a_{n+1}}{a_n}=r forr all n>0.

To find r, note that

\frac{3.2}{16}=\frac{32}{10(16)}=\frac{2}{10}=\frac{1}{5}=0.2

Similarly

\frac{0.64}{3.2}=\frac{64}{10(32)}=\frac{1}{5}=0.2

\frac{0.128}{0.64}=\frac{1}{5}=0.2

Thus a_{n+1}=r a_n=\frac{a_n}{5}=0.2a_n for all n>0, and a_1=16

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