A sequence can be generated by using a n =3a (n-1) where a_{1} = 6 and is a whole number greater than 1. What are the first four terms of the sequence?
To generate the sequence, we start with the first term, which is given as a₁ = 6.
To find the second term, we substitute n = 2 into the formula:
a₂ = 3a(2-1) = 3a₁ = 3(6) = 18.
So, the second term is 18.
To find the third term, we substitute n = 3 into the formula:
a₃ = 3a(3-1) = 3a₂ = 3(18) = 54.
So, the third term is 54.
Finally, to find the fourth term, we substitute n = 4 into the formula:
a₄ = 3a(4-1) = 3a₃ = 3(54) = 162.
So, the fourth term is 162.
Therefore, the first four terms of the sequence are:
6, 18, 54, 162.