Answers

2016-03-26T18:29:10+08:00
12, 15, 21, 30, 42 , 57, 75
The distance between 12 and 15 is 3. The distance between 15 and 21 is 6. The distance between 21 and 30 is 9. So, 3, 6, 9 are from the skip counting of 3. Then, next in the sequence will be 42 because after 9 in the skip counting of 3 is 12 so, you must add 12 to 30 and the answer will be 42 . Add 15 to 42 because 15 comes after 12 in the skip counting of 3 and the sum will be 57, and so on.

15+3=18 -2=16+3=19   so, next will be     19+3=22-2=20+3=23 and so on
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  • Brainly User
2016-03-27T08:53:08+08:00
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:
      T_{n} =  \frac{3}{2}  n^{2}  -  \frac{3}{2} n + 12

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.
            

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