SOLUTION: What is the pattern for the following sequence Term 1,2,3,4,5, n Value 0,3,7,12,18 ? etc.

Question 643336: What is the pattern for the following sequence Term 1,2,3,4,5, n Value 0,3,7,12,18 ? etc.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Use the process of successive differences.

3 minus 0 is 3

7 minus 3 is 4

12 minus 7 is 5

18 minus 12 is 6

Then

4 minus 3 is 1

5 minus 4 is 1

6 minus 5 is 1

Since all of the differences are the same after two passes, you know a quadratic will suffice for a rule (one pass: linear, three passes: cubic, etc.)

So you need a function of the form

Plugging in numbers you get

Which leads to the following 3X3 system:

Which you can solve by your favorite process to get the coefficients of your function.

There is actually a shortcut for sequences. The lead coefficient of your function is always one-half of the value of the value of the constant difference. The constant difference here was 1, so the lead coefficient is 1/2.

John

My calculator said it, I believe it, that settles it

The Out Campaign: Scarlet Letter of Atheism

RELATED QUESTIONS
The formula for the n-th term of this sequence is n2. 1, 4, 9, 16, 25. What is the... (answered by Mathtut,josmiceli)

1) Find the explicit formula that produces the given sequence. 2,-6,18,-54,... A.... (answered by Boreal)

Use the sequence below to write an expression for the nth term term (n) 1 2... (answered by drk)

Use differences to find a pattern in the sequence. -2, -5, -7, -7, -4, 3, 15, What is... (answered by checkley77)

The following function defines a recursive sequence: f(0) = -4 f(1) = 12 f(n) =... (answered by jim_thompson5910)

``write the first six terms of the sequence 2. an=(n+1)^3 4. an=n/n+3 write the... (answered by CubeyThePenguin)

i have selected 10 problems i am having trouble with if anyone could PLEASE help i would... (answered by stanbon)

What is the Nth equation of the following pattern? Figure 1; 3 tiles Figure 2; 5 tiles (answered by scott8148)

I asked this question before, but I did not get all the parts to the uestion posted for... (answered by longjonsilver)