Mastering Summation Notation and Series Formulas

A store sells notebooks for $2 each. If you buy 1 notebook, the total cost is $2. If you buy 2 notebooks, the total cost is $4. Write a summation notation to express the total cost for buying n notebooks. What is the formula for the total cost?

• Total cost = n^2

• Total cost = 2n + 1

• Total cost = 2n

• Total cost = n

A geometric series starts with 3 and each term is multiplied by 2. Write the summation notation for the first 4 terms of this series. What is the formula for the sum of these terms?

• The summation notation is \( \sum_{n=0}^{3} 3 \cdot 2^n \) and the sum of the first 4 terms is 45.

• The summation notation is \( \sum_{n=1}^{4} 3 \cdot 2^n \) and the sum of the first 4 terms is 30.

• The summation notation is \( \sum_{n=0}^{4} 3 \cdot 2^n \) and the sum of the first 4 terms is 60.

• The summation notation is \( \sum_{n=0}^{3} 2 \cdot 3^n \) and the sum of the first 4 terms is 24.

A student scores 5 points on the first test, 10 points on the second, and continues to increase his score by 5 points each test. Write a summation notation for the total score after n tests and convert it to a formula.

• (5n(n + 1))/2

• (5n^2)/2

• (5n^2 + 5n)

• (10n(n + 1))/2

A company’s profit doubles every year, starting with $100 in the first year. Write a summation notation for the profit over 4 years. What is the formula for the total profit after 4 years?

• 1200

• 1500

• 2000

• 1000

A sequence of numbers starts with 1 and each subsequent number increases by 3 (1, 4, 7, ...). Write a summation notation for the first n terms of this sequence and convert it to a formula.

• S_n = 3n(n + 1)/2

• S_n = (3n^2 - n)/2

• S_n = n(3n + 1)/2

• S_n = n^2 + 3n

A person saves $50 in the first month and increases their savings by $10 each month. Write a summation notation for the total savings after 6 months and convert it to a formula.

• 450

• 4500

• 300

• 600

A geometric series has a first term of 5 and a common ratio of 3. Write the summation notation for the first 3 terms and find the sum using the formula for the sum of a geometric series.

• 60

• 65

• 50

• 75

A car travels 100 miles in the first hour and increases its speed by 20 miles each hour. Write a summation notation for the distance traveled in the first 5 hours and convert it to a formula.

• D = 100 + 100 + 100 + 100 + 100 = 500 miles

• D = 100 + 140 + 180 + 220 + 260 = 1000 miles

• D = 100 + 120 + 140 + 160 + 180 = 700 miles

• D = 100 + 110 + 120 + 130 + 140 = 600 miles

A teacher gives 2 extra points for each homework assignment completed. If a student completes n assignments, write a summation notation for the total extra points earned and convert it to a formula.

• 2n^2

• 2n + 1

• 2n

• n