What is the nth term in the sequence:

4, 7, 12, 19, 28

Please show your work.

The nth term in the given sequence will be:
n 2 + 3 ;

Answered by virtuematane | 2024-06-11

The correct answer is n ² +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)n ² , where a is the second difference: (1/2*2)n ² =1n ² .
We now use the term number of each term for n: 4 is the 1st term; 1 1 ² =1. 7 is the 2nd term; 1 2 ² =4. 12 is the 3rd term; 1 3 ² =9. 19 is the 4th term; 1 4 ² =16. 28 is the 5th term: 1*5 ² =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)n ² +d; in our case, 1n ² +d, and since d=3, 1n ² +3.

Answered by MsEHolt | 2024-06-24

The nth term of the sequence 4, 7, 12, 19, 28 is n 2 + 3 . This quadratic formula illustrates how each term is calculated based on its position in the sequence. By substituting the term number into the formula, you can find any term in the sequence.
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Answered by MsEHolt | 2024-09-26