write an explicit formula for the nth term of the sequence 72,12,2

Answer 1

Here you go:

The sequence begins with the following numbers: 72, 12, 2 and we want to determine a general formula for the n^th term of the sequence.

First, we can see that each term in the sequence is the previous term of the sequence divided by 6. How do we write this out explicitly?

If a₁ = 72, then a₂ = 72 / 6 = 12, and a₃ = 12 / 6 = 2. Using this information, we can write out the general formula as follows:

a₁ = 72

for n ≥ 2: {a_n} = (a_n-1 / 6)

Or, shifting the index, the sequence can be written as follows:

a₁ = 72

for n ≥ 1: {a_n+1} = (a_n / 6).

Here {a_n} denotes the sequence beginning with n ≥ 2 and an initial condition a₁ = 72

and {a_n+1} denotes the sequence beginning with n ≥ 1 and an initial condition a₁ = 72

By shifting the index, we are beginning each sequence with the second term after a₁ = 72, but our explicit definition of {a_n} begins when n = 2, and our explicit definition of {a_n+1} begins when n = 1.

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