The nth term of a geometric sequence is given by an = 1/4(4)^n-1. Write the first five terms of this sequence.
t(1) = (1/4)4^1 - 1 = 1 - 1= 0
t(2) = (1/4)(4^2 - 1 = 4 - 1 = 3
t(3) = (1/4)4^3 - 1 = 4^2 - 1 = 15
t(4) = (1/4)4^4 - 1 = 4^3 - 1 = 63
t(5) = ........ = 255
however, if you meant (1/4)4^(n-1) .....?
just sub in and evaluate
okay, thank you
To find the first five terms of the geometric sequence, we can substitute the values of n into the formula an = (1/4)(4)^(n-1).
For n = 1:
a1 = (1/4)(4)^(1-1)
a1 = (1/4)(4)^0
a1 = (1/4)(1)
a1 = 1/4
For n = 2:
a2 = (1/4)(4)^(2-1)
a2 = (1/4)(4)^1
a2 = (1/4)(4)
a2 = 1
For n = 3:
a3 = (1/4)(4)^(3-1)
a3 = (1/4)(4)^2
a3 = (1/4)(16)
a3 = 4
For n = 4:
a4 = (1/4)(4)^(4-1)
a4 = (1/4)(4)^3
a4 = (1/4)(64)
a4 = 16
For n = 5:
a5 = (1/4)(4)^(5-1)
a5 = (1/4)(4)^4
a5 = (1/4)(256)
a5 = 64
Therefore, the first five terms of the geometric sequence are 1/4, 1, 4, 16, and 64.
To find the first five terms of the geometric sequence given by an = 1/4(4)^n-1, we substitute the values of n = 1, 2, 3, 4, and 5 into the formula.
For n = 1:
a1 = 1/4(4)^(1-1)
a1 = 1/4(4)^0
a1 = 1/4 * 1
a1 = 1/4
Therefore, the first term of the sequence is 1/4.
For n = 2:
a2 = 1/4(4)^(2-1)
a2 = 1/4(4)^1
a2 = 1/4 * 4
a2 = 4/4
a2 = 1
Therefore, the second term of the sequence is 1.
For n = 3:
a3 = 1/4(4)^(3-1)
a3 = 1/4(4)^2
a3 = 1/4 * 16
a3 = 16/4
a3 = 4
Therefore, the third term of the sequence is 4.
For n = 4:
a4 = 1/4(4)^(4-1)
a4 = 1/4(4)^3
a4 = 1/4 * 64
a4 = 64/4
a4 = 16
Therefore, the fourth term of the sequence is 16.
For n = 5:
a5 = 1/4(4)^(5-1)
a5 = 1/4(4)^4
a5 = 1/4 * 256
a5 = 256/4
a5 = 64
Therefore, the fifth term of the sequence is 64.
Hence, the first five terms of the given geometric sequence are 1/4, 1, 4, 16, and 64.