Question

What is the explicit rule for the sequence in simplified form?

−1,−4,−7,−10,−13…

Question 12 options:

an=4−5n

an=−4−3n

an=2−3n

an=−6−5n

Answer 1

an = 2 - 3n ⇒ The third answer

Explanation:

∵ a1 = -1

∵ a2 = -4

∵ a3 = -7

∵ a2 - a1 = -4 - -1 = -3

∵ a3 - a2 = -7 - -4 = -3

∴ It is an arithmetic sequence with

1st term = -1 and constant difference = -3

∵ The rule of any arithmetic is: an = a + (n - 1)d

∵ a = -1 and d = -3

∴ an = -1 + (n - 1)(-3)

∴ an = -1 - 3n + 3

∴ an = 2 - 3n ⇒ The third answer