Determining the first five terms of a geometric recursive formula

The video tutorial explains how to find the first five terms of a geometric sequence. It begins by introducing the problem and the formula for a geometric sequence. The instructor then demonstrates how to calculate each term by plugging values into the formula and simplifying the expressions. The tutorial concludes with the final results and a brief discussion on the calculations.

What is the formula for finding the nth term in a geometric sequence?

• a_n = a_1 / r^(n-1)

• a_n = a_1 * n^r

• a_n = a_1 * r^(n-1)

• a_n = a_1 + (n-1) * d

If a_1 = 2 and r = X/4, what is the expression for the second term in the sequence?

• 2 * X/16

• 2 * X/4

• 2 * X/8

• 2 * X/2

How do you simplify the expression 2 * (X/4)^2?

• X^2 / 8

• X^2 / 16

• X^2 / 4

• X^2 / 32

What is the simplified form of 2 * (X/4)^3?

• X^3 / 16

• X^3 / 128

• X^3 / 32

• X^3 / 64

What is the final simplified form of the fifth term in the sequence?

• X^4 / 64

• X^4 / 128

• X^4 / 256

• X^4 / 512