Deriving Rules for Geometric Sequences

What defines a sequence as geometric?

• Dividing each term by a constant to get the next term

• Multiplying each term by a constant to get the next term

• Subtracting the same number from each term

• Adding the same number to each term

What is the common ratio in a geometric sequence?

• The difference between consecutive terms

• The factor by which consecutive terms are multiplied

• The result of dividing any term by its preceding term

• The sum of all terms divided by the number of terms

How can you find the 5th term in a geometric sequence?

• Subtract the common ratio from the 4th term

• Divide the 4th term by the common ratio

• Add the common ratio to the 4th term

• Multiply the 4th term by the common ratio

What does the exponent in the formula for the nth term of a geometric sequence represent?

• The common ratio raised to the power of the term position

• The sum of the term position and the common ratio

• The position of the term in the sequence

• The term position minus one

How do you calculate the 20th term in a geometric sequence using the general rule?

• Multiply the first term by the common ratio 20 times

• Add the common ratio 20 times to the first term

• Multiply the first term by the common ratio raised to the power of 19

• Subtract the common ratio from the first term 19 times

What is the first term in the sequence if the common ratio is 2 and the second term is 12?

• 6

• 12

• 3

• 24

If a sequence has a common ratio of 1/2, what is the 4th term if the first term is 16?

• 1

• 2

• 4

• 8

In a sequence where each term changes sign, what could be the common ratio?

• A positive integer

• A positive fraction

• Zero

• A negative fraction

How do you find the common ratio if the sequence terms are not obvious?

• Divide a term by the previous term

• Multiply consecutive terms

• Subtract consecutive terms

• Add consecutive terms

What is the 100th term of a sequence with a first term of 6 and a common ratio of 2?

• 6 times 2 raised to the 99th power

• 6 times 2 raised to the 100th power

• 6 plus 99 times 2

• 6 times 99