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

an = 2 - 3n ⇒ The third answer

Step-by-step 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