Final answer:
The given sequence 6, 14, 24, 36, 50 is a quadratic sequence because the difference between successive terms increases by a constant amount, which is characteristic of quadratic sequences.
Step-by-step explanation:
The given sequence is 6, 14, 24, 36, 50,... To determine the type of sequence, we need to look at the differences or ratios between the terms.
Let's calculate the differences between successive terms:
- 14 - 6 = 8
- 24 - 14 = 10
- 36 - 24 = 12
- 50 - 36 = 14
We can see that the difference between successive terms is increasing by 2 each time. This is not constant, so it cannot be an arithmetic sequence, where the difference between terms is the same. It is also not a geometric sequence because we are not multiplying by a fixed number to get from one term to the next. The sequence is also not a prime number sequence because not all the numbers are prime (for example, 36). The pattern of differences (8, 10, 12, 14,...) suggests that the sequence is formed by adding consecutive even numbers to the previous term, which is characteristic of a quadratic sequence, where the nth term can be represented by an2 + bn + c.