Understanding Sequences and Simplification

The video tutorial explains how to determine specific terms in a sequence using the formula a sub n equals four n divided by the quantity n plus six. It walks through the process of calculating the first four terms of the sequence, emphasizing the importance of maintaining exact values rather than converting to decimals. Each term is calculated by substituting the respective value of n into the formula, simplifying the expression, and ensuring the result is in its simplest fractional form. The tutorial highlights the significance of understanding the subscript notation and the simplification process.

What is the formula used to determine the terms of the sequence?

• a_n = 4n + 6

• a_n = n/4 + 6

• a_n = n^2 + 4

• a_n = 4n / (n + 6)

What is the value of the first term, a_1, in the sequence?

• 1

• 1/4

• 7/4

• 4/7

Why should we avoid converting the fraction to a decimal when determining a_1?

• Decimals are easier to understand

• Decimals are more accurate

• Fractions provide the exact value

• Fractions are harder to calculate

What is the value of the second term, a_2, in the sequence?

• 1

• 4/8

• 8

• 2

How do you simplify the fraction 8/8?

• Divide both by 1

• Divide both by 8

• Divide both by 2

• Divide both by 4

What is the simplified form of the third term, a_3?

• 9/12

• 3/4

• 4/3

• 12/9

What common factor is used to simplify 12/9?

• 6

• 4

• 2

• 3

What is the value of the fourth term, a_4, in its simplest form?

• 5/8

• 16/10

• 8/5

• 4/5

Which common factor is used to simplify 16/10?

• 4

• 8

• 2

• 5

Why is it important to simplify fractions in this sequence?

• To increase the value of terms

• To convert them to decimals

• To make calculations easier

• To find the exact value of terms