Question

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?

Answer 1

a5 and a71 are 66 places apart
a71 = a5 + 66d
1460 = 74 + 66d
1460 - 74 = 66d
1386 = 66d
1386/66= d
21= d

a5 = a + (5-1)*21
74 = a + 4 * 21
74 = a + 84
74 - 84 = a
-10 = a <=== first term

general term equation : an = -10 + (n-1) * 21

a13 = -10 + (13 - 1) * 21
a13 = -10 + 12*21
a13 = -10 + 252
a13 = 242