
Finding
the Next Number in a Sequence: Sections: Common differences, Recursions, General examples, Nonmath "sequences" What follows are just some additional examples, given so you can see the process at work.
First, I'll see if anything happens to pop out at me. To multiply from 3 to 4, I'd have to multiply by ^{4}/_{3}, but (4)(^{4}/_{3}) does not equal 6, so that must not be the rule. To add from 3 to 4, I'd have to add 1, but 4 + 1 is not 6; 4 + 2 = 6. Wait.... 3 + 1 = 4 Hmm... What if the rule is "add the next bigger number to the last term"? Then I'd have: 9 + 4 = 13 Does this fit? Do I get "18" for the next value? 13 + 5 = 18 Yup; it worked! So it would appear that the rule is "add the next bigger number to the previous term", and: Copyright © Elizabeth Stapel 20022011 All Rights Reserved The missing number is 13. Note that I could have gone straight to the differences:
Since the second differences are the same, then the formula is a quadratic. Plugging in the first three data points, I get: a + b + c = 3 Solving this system of equations, I get: a_{n} = 0.5n^{2} – 0.5n + 3 Plugging in n = 5 for the missing
fifth term, I get: a_{5} = 0.5(25) – 0.5(5) + 3 = 12.5 – 2.5 + 3 = 10 + 3 = 13 So my previous answer was right, or has at least been confirmed as logical.
To add from 4 to 12, I'd have to use 8. To add from 12 to 20, I'd also have to use 8. Let's check to see if "add 8" is the rule: 4 + 8 = 12 It appears that the rule is "add 8". So what is the rule for the nth term? Let's look at the terms: n = 1: 4 Following this pattern, the rule for the nth term will be: a_{n} = 4 + (n – 1)8 << Previous Top  1  2  3  4  5  6  7  Return to Index Next >>


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