Question

# Given the following information about the arithmetic sequence an, find a10. A5=24 a8=39

Answer

49

- Q: What is the formula for finding the nth term of an arithmetic sequence? A: The formula for finding the nth term of an arithmetic sequence is an = a1 + (n-1)d, where a1 is the first term and d is the common difference.
- Q: Can we find the common difference of the given sequence? A: Yes, we can find the common difference using the formula d = a(n) - a(n-1), where n is any term in the sequence.
- Q: What are the values of a5 and a8? A: a5 = 24 and a8 = 39.
- Q: Using the formula for the common difference, what is the value of d? A: d = a8 - a7 = a7 - a6 = 39 - a6. Similarly, d = a6 - a5 = a5 - a4 = a4 - a3. Therefore, we can set these two expressions equal to each other: 39 - a6 = a5 - a4. Substituting in the values of a5 and a6, we get: 39 - ? - d = 24 - ?. Solving for d, we get d = 5.
- Q: Using the formula for the nth term of an arithmetic sequence, what is the value of a10? A: a10 = a1 + (10-1)d. We don't know the value of a1, but we can find it using a5: a5 = a1 + 4d. Substituting in the value of d that we found, we get: 24 = a1 + 20. Therefore, a1 = 4. Now we can find a10: a10 = 4 + 9(5) = 49.