A sequence is defined recursively by the given formulas. Find the first five terms of the sequence.

Question

an =
an − 1
3
and a1 = −12
a1 =
a2 =
a3 =
a4 =
a5 =

Answer 1

To find the first five terms of the sequence, we can use the recursive formula.

Given that a1 = -12, we can find a2 by substituting n = 2 into the formula:
a2 = (a2-1)/3 = (-12)/3 = -4

Similarly, we can find a3 by substituting n = 3:
a3 = (a3-1)/3 = (-4)/3 = -4/3

Continuing this pattern, we can find a4 and a5:
a4 = (a4-1)/3 = (-4/3)/3 = -4/9
a5 = (a5-1)/3 = (-4/9)/3 = -4/27

Therefore, the first five terms of the sequence are:
a1 = -12
a2 = -4
a3 = -4/3
a4 = -4/9
a5 = -4/27