Check the Wronskian determinant:
The determinant is not zero, so the solutions are indeed linearly independent.
Five-eighths inch on a ruler is a mark past 1/2 inch and before 1 inch. If the ruler divides the inches into eighths, 5/8 inch is the fifth mark on the ruler from the left side. If the ruler divides the inches into 16ths, it is the 10th mark.
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. Then:
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.
The correct answer is n²+3
Answer:
<h3> I hoped this helps you ☺️☺️ </h3>
Thank you ☺️☺️
Start by distributing the - 1/3 which is the same as dividing the entire parentheses by 3 which results in (3x+10)