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3 votes
What is the Nth term of
4,7,12,19
ASAP I NEED HELP

User CoreTech
by
7.8k points

1 Answer

6 votes

The correct answer is n²+3.


Explanation:

We find the first differences between terms:

7-4=3; 12-7=5; 19-12=7; 28-19=9.


Since these are different, this is not linear.


We now find the second differences:

5-3=2; 7-5=2; 9-7=2.


Since these are the same, this sequence is quadratic.

We use (1/2a)n², where a is the second difference:

(1/2*2)n²=1n².


We now use the term number of each term for n:

4 is the 1st term; 1*1²=1.

7 is the 2nd term; 1*2²=4.

12 is the 3rd term; 1*3²=9.

19 is the 4th term; 1*4²=16.

28 is the 5th term: 1*5²=25.


Now we find the difference between the actual terms of the sequence and the numbers we just found:


4-1=3; 7-4=3; 12-9=3; 19-16=3; 28-25=3.


Since this is constant, the sequence is in the form (1/2a)n²+d;

in our case, 1n²+d, and since d=3, 1n²+3.

User Sushil Sharma
by
7.8k points

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