Questions and Answers
What is the formula for finding the nth term of an arithmetic sequence?
In the sequence 6, 12, 18, 24, 30, what is the 20th term?
How do you calculate the common difference in an arithmetic sequence?
If the first term of an arithmetic sequence is 11 and the seventh term is 59, what is the common difference?
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What is the 18th term in the arithmetic sequence where the first term is 11 and the common difference is 8?
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In the conference hall example, how many seats are there in the last row?
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If the sequence has a first term of 20 and a common difference of 2, what is the value of the 10th term?
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What process is used to find the 18th term if only the first and seventh terms are given?
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What is the common difference in the arithmetic sequence 11, 18, 25, 32, 39?
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What is the formula for the nth term of an arithmetic sequence?
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What is the 15th term of the arithmetic sequence 16, 20, 24, 28, 32?
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If the first term of an arithmetic sequence is 5 and the common difference is 3, what is the 4th term?
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Determine the nth term of the sequence where a1 = 2 and d = 6.
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What value of n would result in the term being 49 in the sequence starting at 10 with a common difference of 3?
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Study Notes
Arithmetic Sequence
- An arithmetic sequence consists of terms that have a common difference, denoted as d.
- The next term is obtained by adding a constant (d) to the previous term.
Formula for nth Term
- The nth term, an, is calculated by the formula:
( an = a1 + (n - 1) d )
where ( a1 ) is the first term and ( d ) is the common difference.
Example Calculations
- For the sequence 11, 18, 25, 32, 39:
- Common difference ( d = 7 )
- First term ( a1 = 11 )
- nth term formula becomes:
( an = 7n + 4 ) - Confirming:
- ( a1 = 7(1) + 4 = 11 )
- ( a2 = 7(2) + 4 = 18 )
- ( a3 = 7(3) + 4 = 25 )
Finding Specific Terms
- For the sequence 16, 20, 24, 28, 32:
- 15th term calculation:
- First term ( a1 = 16 ), common difference ( d = 4 )
- Using the formula:
( a15 = 16 + (15 - 1) \cdot 4 = 16 + 56 = 72 )
- 15th term calculation:
Determining Term Position
- For the sequence 6, 12, 18, 24, 30, to find which term equals 120:
- Set ( an = 120 ) with ( a1 = 6 ) and ( d = 6 ):
- Result:
120 = 6 + (n - 1) * 6
( n = 20 ) thus, 120 is the 20th term.
- Result:
- Set ( an = 120 ) with ( a1 = 6 ) and ( d = 6 ):
Using Non-Consecutive Terms
- To find the 18th term when given the first term and the 7th term:
- For ( a1 = 11 ) and ( a7 = 59 ):
- Calculate ( d ):
( 59 = 11 + (7 - 1) d ) leads to ( d = 8 ).
- Calculate ( d ):
- Then, find ( a18 ):
- ( a18 = 11 + (18 - 1) \cdot 8 = 147 ).
- For ( a1 = 11 ) and ( a7 = 59 ):
Real-Life Application
- In a conference hall scenario with 20 rows of seats:
- Sequence of seats:
- First row ( a1 = 20 ), increment of ( d = 2 ) per row.
- To find seats in the last row:
- ( a20 = 20 + (20 - 1) \cdot 2 = 20 + 38 = 58 ) seats.
- Sequence of seats:
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Description
Test your knowledge on arithmetic sequences with this quiz. Explore the properties and concepts surrounding this essential mathematical topic. Perfect for students looking to improve their understanding of sequences.
