The simple formula for the nth term of an arithmetic sequence is an = 6n + 14. What is the explicit formula corresponding to the simple formula?
To determine the explicit formula corresponding to the simple formula, we need to expand the term "an" using the given expression "6n + 14." The simple formula represents the general term of an arithmetic sequence, while the explicit formula represents the actual values of the terms in the sequence.
Here's how we can find the explicit formula:
1. Start with the given simple formula: an = 6n + 14.
2. Replace the variable "n" with its corresponding value to get the explicit formula. It is important to note that the n-th term refers to the position of the term in the sequence and is usually represented by a positive integer like 1, 2, 3, and so on.
For example:
- When n = 1, the 1st term is a1, and we have a1 = 6(1) + 14.
- When n = 2, the 2nd term is a2, and we have a2 = 6(2) + 14.
- When n = 3, the 3rd term is a3, and we have a3 = 6(3) + 14.
3. Simplify each equation by performing the necessary multiplication and addition:
- For n = 1: a1 = 6(1) + 14 = 6 + 14 = 20.
- For n = 2: a2 = 6(2) + 14 = 12 + 14 = 26.
- For n = 3: a3 = 6(3) + 14 = 18 + 14 = 32.
4. Write down the values of the terms: a1 = 20, a2 = 26, a3 = 32.
By examining the values we obtained, we can see that the explicit formula for this arithmetic sequence is: a = 20, 26, 32.
Therefore, the explicit formula corresponding to the given simple formula is a = 6n + 14, with the first term being 20, the second term being 26, and so on.