Quadratic sequence: 12, 15, 21, 30, T₅, T₆, T₇.The next three terms (5th, 6th, and 7th) are: 42, 57, 75
The next three terms can be guessed intelligently by following a pattern where the difference between each term
from 1st term to 4th given terms are:
3, 6, 9
Add the next difference (using a pattern through intelligent guess) to the previous term:
Next difference is 12, add to 30 (4th term) yields 42 (the 5th term).
Next difference is 15, add to 42 (5th term) yields 57 (the 6th term).
Next difference is 18, add to 57 (6th term) yields 75 (the 7th term).
But what if we are to find the 20th term, 85th term, 100th term, and so on? This can not be solved immediately by intelligent guess or pattern. We need to find the rule. For the given quadratic sequence 12, 15, 21, 30, the rule is:
Where T = term value
n = nth term in a sequence
Derived from Quadratic equation ax² + bx + c
PLEASE CLICK IMAGE BELOW TO VIEW HOW TO FIND THE RULE AND SOLUTION.