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

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Question 1156485: Write an explicit formula for the sequence.
−4, 8, −28, 80, −244,...
Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

-4, 8,+-28,+80, -244,...

find the pattern:
a%5B1%5D=-4=%28-3%29%5E1-1
a%5B2%5D=8=%28-3%29%5E2-1
a%5B3%5D=-28=%28-3%29%5E3-1
a%5B4%5D=80=%28-3%29%5E4-1
a%5B4%5D=-244=%28-3%29%5E5-1
so, an explicit formula for the sequence is
a%5Bn%5D+=+%28-3%29%5En+-+1 (for all terms given)


Answer by greenestamps(13209) About Me  (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

-4+=+-3-1
8+=+9-1+=+%28-3%29%5E2-1
-28+=+-27-1+=+%28-3%29%5E3-1
80+=+81-1+=+%28-3%29%5E4-1
-244+=+-243-1+=+%28-3%29%5E5-1

The explicit formula is t%28n%29+=+%28-3%29%5En-1