Write the explicit formula for the geometric sequence 2, 8, 32, 128

1 answer:

3 0

The first term, a, is 2. The common ratio, r, is 4. Thus,

a_(n+1) = 2(4)^(n).

Check: What's the first term? Let n=1. Then we get 2(4)^1, or 8. Is that correct? No.

Try this instead:

a_(n) = a_0*4^(n-1). Is this correct? Seeking the first term (n=1), does this formula produce 2? 2*4^0 = 2*1 = 2. YES.

The desired explicit formula is a_(n) = a_0*4^(n-1), where n begins at 1.

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