Geometric Sequence Quiz

This video tutorial explains how to find the general term of a geometric sequence using a system of equations. It demonstrates setting up equations to solve for the first term and common ratio, using substitution to find the common ratio, and calculating the first term. Finally, it derives the general formula for the sequence.

What is the main goal of the problem discussed in the video?

• To find the sum of a geometric sequence

• To determine the general term of a geometric sequence

• To identify the arithmetic mean of a sequence

• To calculate the difference between terms in a sequence

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

• Calculating the sum of terms

• Setting up a system of equations

• Finding the last term

• Identifying the arithmetic mean

Which method is used to solve the system of equations?

• Elimination

• Graphical method

• Matrix method

• Substitution

What is the value of the common ratio 'r' found in the video?

• 2

• 3

• 4

• 5

How is the first term 'a1' determined after finding the common ratio?

• By using the sum of the sequence

• By substituting into one of the given terms

• By using the difference between terms

• By calculating the average of terms

What is the formula for the general term 'a_n' of the sequence?

• a_n = a1 - r^(n-1)

• a_n = a1 / r^(n-1)

• a_n = a1 * r^(n-1)

• a_n = a1 + r^(n-1)

What is the value of 'a1' found in the video?

• 7/243

• 7/81

• 7/27

• 7/9

Which term is used to verify the value of 'a1'?

• a3

• a12

• a6

• a9

What is the exponent used in the formula for the general term?

• n+1

• n-1

• n

• n-2

What is the final expression for the general term 'a_n'?

• a_n = 7/243 * 3^(n-1)

• a_n = 7/243 * 2^(n-1)

• a_n = 7/243 * 5^(n-1)

• a_n = 7/243 * 4^(n-1)