The first term in an arithmetic sequence is 5. The second term in the sequence is 8. What is the explicit rule? What is the 25th term?
A. an= 5 + (n – 1)(-3); -67
B. an = 2 + (n – 1)(3); 74
C.an = 5 + (n – 1)(3); 77
D.an = 2 + (n – 1)(-3); -70
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To find the explicit rule for an arithmetic sequence, we need to determine the common difference (d) between consecutive terms.
Given the information that the first term is 5 and the second term is 8, we can calculate the common difference by subtracting the first term from the second term:
d = 8 - 5 = 3
Once we have the common difference, we can write the explicit rule in the form an = a1 + (n - 1)d, where an is the nth term, a1 is the first term, n is the position of the term in the sequence, and d is the common difference.
Using the values we have, the explicit rule becomes:
an = 5 + (n - 1)(3)
Now, to find the 25th term, substitute n = 25 into the explicit rule:
a25 = 5 + (25 - 1)(3)
= 5 + 24(3)
= 5 + 72
= 77
Therefore, the explicit rule is an = 5 + (n - 1)(3), and the 25th term is 77.
Therefore, the correct answer is C. an = 5 + (n - 1)(3); 77.