What is the explicit formula for this geometric sequence? 8, 4, 2, 1

a[n] = 2^ (4-n)

Step-by-step explanation:

There are many ways the formula for the given sequence can be written. The first term (a[1]) is 8 and the common ratio (r) is 1/2, so the generic form is ...

a[n] = a[1]·r^ (n-1)

a[n] = 8· (1/2) ^ (n-1)

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If we recognize that 8 = 2^3 and 1/2 = 2^-1, then we can write this as ...

a[n] = 2^3· (2^-1) ^ (n-1) = 2^ (3 - n + 1)

a[n] = 2^ (4 - n)