Consider a sequence whose first three

terms are 27,21,15 ... Write an equation

for this sequence in explicit form.

Below, depends if 27 is term number 1 or term number 0. Answered for both cases.

Step-by-step explanation:

The most common sequences are arithmetic and geometric, so lets check those first.

Arithmetic first since its the easiest.

to go from 27 to 21 we subtract 6, if we subtract 6 from 21 again we get to 15, which is what we need, so it is indeed arithmetic.

Explicit formula is basically of the form of y=mx+b with an arithmetic sequence. the m is the common difference and b is the first term minus the common difference. so lets fill those in. y = - 6x + 33

Then it usually has n as the x and y f (n) so we'll just put those in

f (n) = - 6n + 33

This si as long as the first term is labeled as term number 1 and not term number 0. if you have 27 as term 0 instead just make 33 back to 27, so f (n) = - 6n + 27

Let me know if this doesn't make sense.