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Find an equation for the nth term in the following sequence:
2, 8, 32, 128, 512...

2 Answers

2 votes

Answer:

nth term of the sequence is
2^(2n-1) or
T_(n)=2.(4)^(n-1)

Explanation:

The given sequence is 2, 8, 32, 128, 512.........

Or we can rewrite the sequence as
2, 2^(3), 2^(5),2^(7),2^(9) ,...............nth term.

Now the new form of sequence confirms that the sequence is an exponential sequence.

Therefore nth term of the sequence will be
T_(n)=2^(2n-1) Or
T_(n)=2.(4)^(n-1)

User Onupdatecascade
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0 votes

Answer:


a_n = 2(4) ^(n-1)

Explanation:

The sequence shown matches that of a geometric sequence of radius 4. To prove it, divide the term
(a_(n + 1))/(a_n) and check that
(a_(n + 1))/(a_n)=4

Then the formula that represents this sequence is:


a_n = a_1(r)^(n-1)

Where
a_1 is the first term of the series = 2 and
r is the radius of convergence = 4.

Then the equation is:


a_n = 2(4) ^(n-1)

User LicenseQ
by
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