Given the explicit formula: a5= 8 + (5 − 1)3
What is the common difference? Response area
What is the initial term? Response area
What term is the formula finding? Response area
The common difference is 3.
The initial term is 8.
The formula is finding the 5th term.
To find the common difference, initial term, and term being found using the explicit formula, let's analyze the given formula a₅ = 8 + (5 - 1)3.
1. Common Difference:
In an arithmetic sequence, the common difference is the fixed value that is added (or subtracted) to each term to get to the next term. In this case, the formula a₅ = 8 + (5 - 1)3 represents the fifth term of the sequence. The difference between the fifth term and the fourth term is given by (5 - 1)3, which simplifies to 4 × 3 = 12. Therefore, the common difference is 12.
2. Initial Term:
To determine the initial term, we need to find the first term of the sequence. Since the formula given represents the fifth term (a₅), we can use the formula for the nth term of an arithmetic sequence to find the first term. By substituting n = 1 into the formula, we will have a₁ = 8 + (1 - 1)3, which simplifies to a₁ = 8 + 0 = 8. Hence, the initial term is 8.
3. Term Being Found:
The formula a₅ = 8 + (5 - 1)3 explicitly represents the fifth term of the sequence. Therefore, the term being found using this formula is the fifth term (a₅).
To summarize:
- Common Difference: 12
- Initial Term: 8
- Term Being Found: Fifth Term (a₅)
The common difference in the given explicit formula is 3.
The initial term, also known as the first term, is 8.
The given formula is finding the 5th term in the sequence.