Find the first five terms of the sequence defined below, where n represents the position of a term in the sequence. Start with n = 1.
an = 3(4)n
The first term (n = 1) is found by plugging 1 into the formula: a1 = 3(4)(1) = 12.
The second term (n = 2) is found by plugging 2 into the formula: a2 = 3(4)(2) = 24.
The third term (n = 3) is found by plugging 3 into the formula: a3 = 3(4)(3) = 36.
The fourth term (n = 4) is found by plugging 4 into the formula: a4 = 3(4)(4) = 48.
The fifth term (n = 5) is found by plugging 5 into the formula: a5 = 3(4)(5) = 60.
Therefore, the first five terms of the sequence are: 12, 24, 36, 48, 60.
To find the first five terms of the sequence defined by the formula an = 3(4)n, we substitute the values of n from 1 to 5.
For n = 1:
a1 = 3(4)^1
a1 = 3(4)
a1 = 12
For n = 2:
a2 = 3(4)^2
a2 = 3(16)
a2 = 48
For n = 3:
a3 = 3(4)^3
a3 = 3(64)
a3 = 192
For n = 4:
a4 = 3(4)^4
a4 = 3(256)
a4 = 768
For n = 5:
a5 = 3(4)^5
a5 = 3(1024)
a5 = 3072
Therefore, the first five terms of the sequence are:
a1 = 12
a2 = 48
a3 = 192
a4 = 768
a5 = 3072