All Common Core: High School - Algebra Resources
Example Questions
Example Question #61 : Seeing Structure In Expressions
Identify the following sequence as arithmetic, geometric, or neither.
Neither
Arithmetic
Geometric
Arithmetic
To identify the sequence as either arithmetic or geometric, first recall the difference between the two. An arithmetic sequence means there exists a common difference between the terms. If a sequence is geometric, then there exists a common ratio between the terms.
Looking at the given sequence,
subtract the first term from the second term to find the common difference.
From here, add the common difference to the second term. If the sum is the third term, then the sequence is arithmetic.
Adding the common difference to each term in the sequence results in the next term in the sequence which makes this particular sequence, arithmetic.
Example Question #62 : Seeing Structure In Expressions
Identify the following sequence as arithmetic, geometric, or neither.
Geometric
Arithmetic
Neither
Arithmetic
To identify the sequence as either arithmetic or geometric, first recall the difference between the two. An arithmetic sequence means there exists a common difference between the terms. If a sequence is geometric, then there exists a common ratio between the terms.
Looking at the given sequence,
subtract the first term from the second term to find the common difference.
From here, add the common difference to the second term. If the sum is the third term, then the sequence is arithmetic.
Adding the common difference to each term in the sequence results in the next term in the sequence which makes this particular sequence, arithmetic.
Example Question #63 : Seeing Structure In Expressions
Identify the following sequence as arithmetic, geometric, or neither.
Geometric
Neither
Arithmetic
Neither
To identify the sequence as either arithmetic or geometric, first recall the difference between the two. An arithmetic sequence means there exists a common difference between the terms. If a sequence is geometric, then there exists a common ratio between the terms.
Looking at the given sequence,
subtract the first term from the second term to find the common difference.
From here, add the common difference to the second term. If the sum is the third term, then the sequence is arithmetic.
If adding the common difference to each term in the sequence results in next term then the sequence is arithmetic.
All terms except for the third term follow this therefore, the sequence is neither arithmetic nor geometric.
Example Question #64 : Seeing Structure In Expressions
Identify the following sequence as arithmetic, geometric, or neither.
Neither
Geometric
Arithmetic
Neither
To identify the sequence as either arithmetic or geometric, first recall the difference between the two. An arithmetic sequence means there exists a common difference between the terms. If a sequence is geometric, then there exists a common ratio between the terms.
Looking at the given sequence,
subtract the first term from the second term to find the common difference.
From here, add the common difference to the second term. If the sum is the third term, then the sequence is arithmetic.
If adding the common difference to each term in the sequence results in next term then the sequence is arithmetic.
All terms except for the third term follow this therefore, the sequence is neither arithmetic nor geometric.
Example Question #65 : Seeing Structure In Expressions
Identify the following sequence as arithmetic, geometric, or neither.
Neither
Geometric
Arithmetic
Neither
To identify the sequence as either arithmetic or geometric, first recall the difference between the two. An arithmetic sequence means there exists a common difference between the terms. If a sequence is geometric, then there exists a common ratio between the terms.
Looking at the given sequence,
subtract the first term from the second term to find the common difference.
From here, add the common difference to the second term.
If adding the common difference to each term in the sequence results in next term then the sequence is arithmetic.
All terms except for the fourth term follow this therefore, the sequence is neither arithmetic nor geometric.
Example Question #66 : Seeing Structure In Expressions
Identify the following sequence as arithmetic, geometric, or neither.
Arithmetic
Geometric
Neither
Geometric
To identify the sequence as either arithmetic or geometric, first recall the difference between the two. An arithmetic sequence means there exists a common difference between the terms. If a sequence is geometric, then there exists a common ratio between the terms.
Looking at the given sequence,
divide the second term by the first term to find the common ratio.
From here, multiply the common ratio by each term to get the next term in the sequence.
Since each term is found by multiplying the common ratio with the previous term, the sequence is known as a geometric one.
Example Question #67 : Seeing Structure In Expressions
Identify the following sequence as arithmetic, geometric, or neither.
Geometric
Arithmetic
Neither
Geometric
To identify the sequence as either arithmetic or geometric, first recall the difference between the two. An arithmetic sequence means there exists a common difference between the terms. If a sequence is geometric, then there exists a common ratio between the terms.
Looking at the given sequence,
divide the second term by the first term to find the common ratio.
From here, multiply the common ratio by each term to get the next term in the sequence.
Since each term is found by multiplying the common ratio with the previous term, the sequence is known as a geometric one.
Example Question #68 : Seeing Structure In Expressions
Identify the following sequence as arithmetic, geometric, or neither.
Geometric
Neither
Arithmetic
Geometric
To identify the sequence as either arithmetic or geometric, first recall the difference between the two. An arithmetic sequence means there exists a common difference between the terms. If a sequence is geometric, then there exists a common ratio between the terms.
Looking at the given sequence,
divide the second term by the first term to find the common ratio.
From here, multiply the common ratio by each term to get the next term in the sequence.
Since each term is found by multiplying the common ratio with the previous term, the sequence is known as a geometric one.
Example Question #69 : Seeing Structure In Expressions
Identify the following sequence as arithmetic, geometric, or neither.
Arithmetic
Neither
Geometric
Arithmetic
To identify the sequence as either arithmetic or geometric, first recall the difference between the two. An arithmetic sequence means that there is a common difference between the terms. If a sequence is geometric, then there is a common ratio between the terms.
Looking at the given sequence,
subtract the first term from the second term to find the common difference.
From here, add the common difference to the second term. If the sum is the third term, then the sequence is arithmetic.
Adding the common difference to each term in the sequence results in the next term in the sequence which makes this particular sequence, arithmetic.
Example Question #70 : Seeing Structure In Expressions
Identify the following series as arithmetic, geometric, or neither.
100, 200, 300, 400, 500...
Arithmetic
Geometric
Neither
Arithmetic
This is an arithmetic sequence. Note that the same number (100) is added to each value in the set to give us our next number:
100
100 + 100 = 200
200 + 100 = 300
300 + 100 = 400
400 + 100 = 500
When the same value is added to each term to determine the next one, that is an arithmetic sequence.