Understanding Recursive Sequences

The video tutorial explains how to find terms in a sequence using a recursive formula. It starts with defining the sequence and then demonstrates the calculation of subsequent terms, a sub 2, a sub 3, and a sub 4, using the recursive formula. The process involves substitution, finding common denominators, and performing arithmetic operations to derive each term.

What is the initial term (a sub one) in the given recursive sequence?

• 3

• 0

• 1

• 2

How is the second term (a sub two) calculated in the sequence?

• By adding 3 to the first term

• By subtracting 3 from the first term

• By dividing 4 by the first term and adding 3

• By multiplying the first term by 4

What is the value of the second term (a sub two) in the sequence?

• 5

• 6

• 7

• 8

To find the third term (a sub three), what common denominator is used?

• 6

• 8

• 5

• 7

What is the value of the third term (a sub three) in the sequence?

• 22/7

• 23/7

• 24/7

• 25/7

How is division by a fraction handled when calculating the fourth term?

• By adding the reciprocal

• By subtracting the reciprocal

• By multiplying by the reciprocal

• By dividing by the reciprocal

What is the reciprocal of 25/7 used in the calculation of the fourth term?

• 7/25

• 1/7

• 1/25

• 25/7

What is the least common denominator used in the final steps of calculating the fourth term?

• 35

• 20

• 25

• 30

What is the final value of the fourth term (a sub four) in the sequence?

• 100/25

• 101/25

• 102/25

• 103/25

What is the main purpose of using a recursive formula in sequences?

• To identify the largest term

• To calculate the average of terms

• To determine each term based on the previous one

• To find the sum of all terms