Mastery Check - Arithmetic and Geometric Sequences and Series - Fernando Hernandez | Library

Learning Target (LT1): I will find the nth term of an arithmetic sequence and series.
Learning Target (LT2): I will find the nth term of a geometric sequence and series.
Learning Target (LT3): I will find the sum of arithmetic and geometric sequences and series
Learning Target (LT4): I will find the sum of an infinite geometric sequence.

LEVEL 2 (Must complete. Maximum score: 75%)

4

A teacher earns an annual salary of $45,000 for the first year of her employment. Her annual salary increases by $1,750 each year. (LT1)

a. What is the common difference?
b. Calculate the total salary she earns in this employment for the first 10 years.

2

Evaluate the following. Must show work. (LT3)

4

Find the first five terms of a geometric sequences if the third term is -135 and the fourth term is 405. (LT2)

2

Determine if the infinite geometric series is convergent or divergent. If convergent, find the limit.

LEVEL 3 (Must complete LEVEL 2. Maximum score: 90%)

4

The sum of the first n terms of this sequence is
a. Find the sum of the first 100 terms in this arithmetic sequence. (LT3)
b. The sum of the first n terms is 477. Find the number of terms. (LT3)

4

The seventh term of a geometric sequence is 108. The eighth term is 36. (LT2)

a. Find the first term.
b. The sum of the first n terms in the sequences is 118096. Find n.

5

A theater has a total of 26 rows. The first row has 18 seats. The second row has 20 seats. The third row has 22 seats. The pattern for seats in each row continues.

a. Write an expression for the total number of seats in the first n rows.
b. Calculate the seating capacity of the theater.

0

Find the value(s) of x which allow the infinite geometric series to converge.

Level 4 (Must complete LEVEL 2 and LEVEL 3. Maximum score: 100%)

4

Two sequences have the same common difference. How many terms could the sequences have in common? Justify your answer. (LT1)

6

A geometric sequence has all positive numbers. The sum of the first two terms is 15 and the sum to infinity is 27. (LT3)(LT4)

a. Find the common ratio.
b. Find the first term.

Mastery Check - Arithmetic and Geometric Sequences and Series

A teacher earns an annual salary of $45,000 for the first year of her employment. Her annual salary increases by $1,750 each year. (LT1)a. What is the common difference?b. Calculate the total salary she earns in this employment for the first 10 years.

Evaluate the following. Must show work. (LT3)

Find the first five terms of a geometric sequences if the third term is -135 and the fourth term is 405. (LT2)

Determine if the infinite geometric series is convergent or divergent. If convergent, find the limit.

The sum of the first n terms of this sequence isa. Find the sum of the first 100 terms in this arithmetic sequence. (LT3)b. The sum of the first n terms is 477. Find the number of terms. (LT3)

The seventh term of a geometric sequence is 108. The eighth term is 36. (LT2)a. Find the first term.b. The sum of the first n terms in the sequences is 118096. Find n.

A theater has a total of 26 rows. The first row has 18 seats. The second row has 20 seats. The third row has 22 seats. The pattern for seats in each row continues.a. Write an expression for the total number of seats in the first n rows.b. Calculate the seating capacity of the theater.

Find the value(s) of x which allow the infinite geometric series to converge.

Two sequences have the same common difference. How many terms could the sequences have in common? Justify your answer. (LT1)

A geometric sequence has all positive numbers. The sum of the first two terms is 15 and the sum to infinity is 27. (LT3)(LT4)a. Find the common ratio.b. Find the first term.

A teacher earns an annual salary of $45,000 for the first year of her employment. Her annual salary increases by $1,750 each year. (LT1)

a. What is the common difference?
b. Calculate the total salary she earns in this employment for the first 10 years.

The sum of the first n terms of this sequence is
a. Find the sum of the first 100 terms in this arithmetic sequence. (LT3)
b. The sum of the first n terms is 477. Find the number of terms. (LT3)

The seventh term of a geometric sequence is 108. The eighth term is 36. (LT2)

a. Find the first term.
b. The sum of the first n terms in the sequences is 118096. Find n.

A theater has a total of 26 rows. The first row has 18 seats. The second row has 20 seats. The third row has 22 seats. The pattern for seats in each row continues.

a. Write an expression for the total number of seats in the first n rows.
b. Calculate the seating capacity of the theater.

A geometric sequence has all positive numbers. The sum of the first two terms is 15 and the sum to infinity is 27. (LT3)(LT4)

a. Find the common ratio.
b. Find the first term.