Geometric Sequences and Powers

The video tutorial explains the geometric sequence Asobi, defined by a specific formula. It guides viewers through calculating the fifth term of the sequence using the formula, emphasizing the impact of raising negative numbers to even powers, which results in a positive value. The tutorial concludes with the final calculation, showing that the fifth term is positive 3 over 256.

What is the formula used to define the geometric sequence in the video?

• a_n = 3 * (-1/4)^(n-1)

• a_n = 3 * (1/4)^n

• a_n = 3 * (1/4)^(n-1)

• a_n = 3 * (-1/4)^n

What is the first step in finding the fifth term of the sequence?

• Divide 3 by 5

• Add 5 to the formula

• Substitute 5 for n in the formula

• Multiply 3 by -1/4

What power is used in the calculation of the fifth term?

• Second power

• Fifth power

• Third power

• Fourth power

Why does the result of the fifth term calculation become positive?

• Because the base is positive

• Because the exponent is odd

• Because the exponent is even

• Because the base is zero

What is the final value of the fifth term in the sequence?

• 3/64

• 3/128

• 3/256

• 3/512

What is the significance of raising a negative number to an even power?

• It results in a positive number

• It results in zero

• It results in an undefined number

• It results in a negative number

What is the base number used in the power calculation for the fifth term?

• 1/2

• 1/3

• 1/4

• 1/5