+117 Consider the arithmetic sequence presented in the table below.
n 57 1
an 74 1,460
Hint: an = a1 + d(n − 1), where a1 is the first term and d is the common difference.
Part A: What is the first term, a1, of the sequence?
Part B: What is the general term equation, an, for this sequence?
Part C: What is the value of the 13th term of this sequence?
+129852 A. 1st term = 1460
B. We need to solve this
74 = 1460 + d(57 -1)
74 = 1460 + d(56) subtract 1460 from both sides
-1386 = 56d divide both sides by 56
d = -24.75
So the general equation is
an = 1460 - 24.75(n - 1)
C. The 13th term is
1460 -24.75(13 -1) = 1460 -24.75(12) = 1163
