Answer:
a^1=1
a^8=16,384
Step-by-step explanation:
The original equation of a^n=4^n-1 uses n as a placeholder variable for whatever value is needed to solve the equation. For the first question, which gives 1=n, substituting 1 into the equation gives you the answer of 1. 1-1=0. You can not have any number to the power of zero however, so due to the multiplicative identity, you end up with a positive 1.
The second one we are given 8=n. 8-1 equal 7. 4 to the power of seven (multiply 4 by itself 7 times) gets you 16, 384.
Given the sequence defined as [tex]a_{n} = 4n - 1[/tex], [tex]a_{1} =3\ and\ a _ {8} = 31[/tex].
An arithmetic sequence is a sequence where each term increases by adding/subtracting some constant k.
[tex]a_{n} = a_{1} + (n-1)d[/tex]
Given sequence:
[tex]a_{n} = 4n - 1\\\\a_{1} = 4 * 1 - 1 = 4 - 1 =3\\\\a _ {8} = 4 * 8 - 1 = 32 - 1 = 31[/tex]
Learn more about arithmetic sequence here
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