SOLUTION: Write an explicit formula for the sequence. −4, 8, −28, 80, −244,...

Question 1156485: Write an explicit formula for the sequence.
−4, 8, −28, 80, −244,...

Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

, ,,, ,...

find the pattern:

so, an explicit formula for the sequence is
(for all terms given)

Answer by greenestamps(13214) (Show Source): You can put this solution on YOUR website!

The other tutor showed the pattern; she provided no insight into HOW to FIND the pattern.

Here is a bit to try to help you with that.

(1) Ignore the alternating signs for now; we can take care of that later.

(2) The numbers are now 4, 8, 28, 80, 244. The ratio from one number to the next is always about 3 to 1. And the numbers are now all close to consecutive powers of 3: 3, 9, 27, 81, 243.
4, 8, 28, 80, 243 3, 9, 27, 81, 244

(3) Now put the negative signs back in both sequences and compare them:
-4, 8, -28, 80, -244 -3, 9, -27, 81, -243

The explicit formula is

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