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Questions and Answers
In an arithmetic sequence, if the first term is 5 and the common difference is 3, what is the value of the 10th term?
In an arithmetic sequence, if the first term is 5 and the common difference is 3, what is the value of the 10th term?
- 35
- 26
- 28
- 32 (correct)
An arithmetic sequence has a common difference of -2. If the 4th term is 10, what is the first term of the sequence?
An arithmetic sequence has a common difference of -2. If the 4th term is 10, what is the first term of the sequence?
- 18
- 16 (correct)
- 14
- 12
In a given arithmetic sequence, the 3rd term is 7 and the 7th term is 15. What is the common difference of the sequence?
In a given arithmetic sequence, the 3rd term is 7 and the 7th term is 15. What is the common difference of the sequence?
- 2 (correct)
- 1
- 3
- 4
If the first term of an arithmetic sequence is -3, and the 6th term is 12, what term number has a value of 27?
If the first term of an arithmetic sequence is -3, and the 6th term is 12, what term number has a value of 27?
Which formula accurately calculates the position n of a term with value Tn in an arithmetic sequence, given the first term a and common difference d?
Which formula accurately calculates the position n of a term with value Tn in an arithmetic sequence, given the first term a and common difference d?
Flashcards
Arithmetic Sequence
Arithmetic Sequence
A sequence where the difference between consecutive terms is constant.
Common Difference ('d')
Common Difference ('d')
The constant value added to each term in an arithmetic sequence. Represented by 'd'.
Arithmetic Sequence Formula
Arithmetic Sequence Formula
Tâ‚™ = a + (n - 1) * d a = first term, n = term position, d = common difference, Tâ‚™ = value at position n
First Term ('a')
First Term ('a')
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Term Position ('n')
Term Position ('n')
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Study Notes
- Arithmetic sequences have a constant difference between consecutive numbers.
- The difference between 23 and 25 is 2.
- The difference between 13 and 15 is 2.
Arithmetic Sequence Formula
arepresents the first term in the sequence.nis the position number of a term in the sequence.dis the constant difference between consecutive terms.Tn(Tâ‚™) is the value of the term at positionn.- The number 9 is at position 1.
- The number 19 is at position 6.
- The number 25 is at position 9 and has a value of 25.
Formula Application
- To find the value of the term at position 7:
- T₇ = a + (7 - 1) * d
- T₇ = 9 + (6) * 2 = 9 + 12 = 21
- Using the formula in reverse, the position of a term with a known value can be found.
Reverse Formula Application
- Given a term with a value of 17, we want to find its position (n).
- 17 = 9 + (n - 1) * 2
- 8 = (n - 1) * 2
- Dividing both sides by 2: 4 = n - 1
- Solving for n: n = 5
- The value of 17 is at position 5 in the sequence.
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