Final answer:
The nth term of the sequence 0, 5, 10, 15, 20 is given by the formula Tn = 5(n - 1), where Tn is the nth term and n is the position number in the sequence.
Step-by-step explanation:
To determine the nth term of the sequence 0, 5, 10, 15, 20, we need to find a pattern that describes how each term is generated from its position number (n). We can see that each term increases by 5 from the previous term. Therefore, the difference between consecutive terms is constant, which indicates this is an arithmetic sequence.
The first term (0) is what you would get if you multiplied n by 0, since 5 times 0 is 0. To get to the subsequent terms, you add 5, 10, 15, and so on. So, the nth term is 5 times (n-1). Put mathematically, it's Tn = 5(n - 1) where Tn is the nth term and n is the position number in the sequence.
Step-by-step explanation:
- Determine the common difference (d) by subtracting a term from the term that follows it. For this sequence: 5 - 0 = 5.
- Write down the formula for the nth term of an arithmetic sequence: Tn = a + (n - 1)d.
- In the formula, 'a' is the first term, which is 0, and 'd' is the common difference, which we found to be 5. Plug these values into the formula.
- Therefore, the nth term is Tn = 0 + (n - 1)*5 = 5(n - 1).