# 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.