SOLUTION: The first 4 terms of an arithmetic sequence are 187, 173, 159, and 145. a. Give an explicit formula for this sequence. b. Give a recursive formula for this sequence.

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Okay, if our sequence is 187, 173, 159, 145, we can see that our common difference is -14, that is, each term is 14 less than the one before it...
The explicit formula looks like this
A-sub-n = 187 - 14(n-1) where n is the nth term of the sequence
A recursive relationship here shows how the (n + 1)th term is related to the nth term...here we have
A-sub-n+1 = A-sub-n - 14
Now for the geometric sequence 3, -54, 972, we can see that we are multiplying each successive term by -18...thus the explicit formula looks like this:
A-sub-n = 3(-18)^(n-1) and the recursive form is
A-sub-n+1 = (-18) times A-sub-n
where n is the nth term of the sequence