Consider the arithmetic sequence presented in the table below.
n 5 71
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?
+130518 74 = a1 + d(5 - 1) → 74 = a1 + 4d (1)
1460 = a1 + d(71 - 1) → 1460 = a1 + 70d (2)
Subtract (1) from (2)
1386 = 66d divide both sides by 66
21 = d
Using (1)
74 = a1 + 21(4)
74 = a1 + 84 subtract 84 from both sides
-10 = a1
The general formula is :
an = -10 + 21(n - 1)
13th term =
-10 + 21 (13 - 1)
-10 + 21 (12) =
242
