Mastery Check - Arithmetic and Geometric Sequences and Series

Last updated over 5 years ago

10 questions

Mastery Check - Arithmetic and Geometric Sequences and Series

Last updated over 5 years ago

10 questions

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%)

You open a savings account with $500. The following month, you deposit $100; and the month after that, you deposit $250.

a. What is the common ratio?
b. How much money will you have in your account at the end of 5 years?

Evaluate the following. Must show work. (LT3)

Find the first five terms of an arithmetic sequence 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.

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

The sum of the first n terms of this sequence is
a. Find the sum of the first 200 terms in this arithmetic sequence. (LT3)
b. The sum of the first n terms is 4030. Find the number of terms. (LT3)

The seventh term of a geometric sequence is 108. The tenth term is 4. (LT2)

a. Find the first term.
b. The sum of the first n terms in the sequences is 708600. Find n.

You build a pyramid out of toy bricks. The top row contains one brick. The second row contains three bricks. Each row beneath that contains two more bricks than the row above.

a. How many bricks does the nth row (from the top) contain?
b. If a total of 36 bricks are used, how many rows are there?

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%)

Do the even-numbered terms of an infinite geometric sequence form another infinite geometric sequence? Justify your answer.

A geometric sequence and an arithmetic sequence both have 1 as their first term. The third term of the arithmetic sequence is the same as the second term of the geometric sequence. The fourth term of the arithmetic sequence is the same as the third term of the geometric sequence. Find all the possible values of the common difference of the arithmetic sequence.

Mastery Check - Arithmetic and Geometric Sequences and Series

Mastery Check - Arithmetic and Geometric Sequences and Series

You open a savings account with $500. The following month, you deposit $100; and the month after that, you deposit $250.a. What is the common ratio?b. How much money will you have in your account at the end of 5 years?

Evaluate the following. Must show work. (LT3)

Find the first five terms of an arithmetic sequence 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 200 terms in this arithmetic sequence. (LT3)b. The sum of the first n terms is 4030. Find the number of terms. (LT3)

The seventh term of a geometric sequence is 108. The tenth term is 4. (LT2)a. Find the first term.b. The sum of the first n terms in the sequences is 708600. Find n.

You build a pyramid out of toy bricks. The top row contains one brick. The second row contains three bricks. Each row beneath that contains two more bricks than the row above.a. How many bricks does the nth row (from the top) contain?b. If a total of 36 bricks are used, how many rows are there?

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

Do the even-numbered terms of an infinite geometric sequence form another infinite geometric sequence? Justify your answer.

You open a savings account with $500. The following month, you deposit $100; and the month after that, you deposit $250.a. What is the common ratio?b. How much money will you have in your account at the end of 5 years?

Evaluate the following. Must show work. (LT3)

Find the first five terms of an arithmetic sequence 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 200 terms in this arithmetic sequence. (LT3)b. The sum of the first n terms is 4030. Find the number of terms. (LT3)

The seventh term of a geometric sequence is 108. The tenth term is 4. (LT2)a. Find the first term.b. The sum of the first n terms in the sequences is 708600. Find n.

You build a pyramid out of toy bricks. The top row contains one brick. The second row contains three bricks. Each row beneath that contains two more bricks than the row above.a. How many bricks does the nth row (from the top) contain?b. If a total of 36 bricks are used, how many rows are there?

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

Do the even-numbered terms of an infinite geometric sequence form another infinite geometric sequence? Justify your answer.

You open a savings account with $500. The following month, you deposit $100; and the month after that, you deposit $250.

a. What is the common ratio?
b. How much money will you have in your account at the end of 5 years?

The sum of the first n terms of this sequence is
a. Find the sum of the first 200 terms in this arithmetic sequence. (LT3)
b. The sum of the first n terms is 4030. Find the number of terms. (LT3)

The seventh term of a geometric sequence is 108. The tenth term is 4. (LT2)

a. Find the first term.
b. The sum of the first n terms in the sequences is 708600. Find n.

You build a pyramid out of toy bricks. The top row contains one brick. The second row contains three bricks. Each row beneath that contains two more bricks than the row above.

a. How many bricks does the nth row (from the top) contain?
b. If a total of 36 bricks are used, how many rows are there?

You open a savings account with $500. The following month, you deposit $100; and the month after that, you deposit $250.

a. What is the common ratio?
b. How much money will you have in your account at the end of 5 years?

The sum of the first n terms of this sequence is
a. Find the sum of the first 200 terms in this arithmetic sequence. (LT3)
b. The sum of the first n terms is 4030. Find the number of terms. (LT3)

The seventh term of a geometric sequence is 108. The tenth term is 4. (LT2)

a. Find the first term.
b. The sum of the first n terms in the sequences is 708600. Find n.

You build a pyramid out of toy bricks. The top row contains one brick. The second row contains three bricks. Each row beneath that contains two more bricks than the row above.

a. How many bricks does the nth row (from the top) contain?
b. If a total of 36 bricks are used, how many rows are there?