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Questions and Answers
Which of the following is the correct equation to find the nth term of an arithmetic progression?
Which of the following is the correct equation to find the nth term of an arithmetic progression?
- $a_n = a_1 + (n + 1)d$
- $a_n = a_1 \cdot (n - 1)d$
- $a_n = a_1 \cdot (n + 1)d$
- $a_n = a_1 + (n - 1)d$ (correct)
Which term of the arithmetic progression 2, 5, 8, 11, ... is 23?
Which term of the arithmetic progression 2, 5, 8, 11, ... is 23?
- $a_7$
- $a_9$
- $a_8$ (correct)
- $a_6$
What is the common difference of the arithmetic progression 10, 7, 4, 1, ...?
What is the common difference of the arithmetic progression 10, 7, 4, 1, ...?
- $-3$ (correct)
- $-1$
- $-2$
- $3$
What is the sum of the arithmetic series 3, 6, 9, 12, ..., 99?
What is the sum of the arithmetic series 3, 6, 9, 12, ..., 99?
According to the anecdote, who reinvented the method to compute arithmetic progressions?
According to the anecdote, who reinvented the method to compute arithmetic progressions?
Flashcards
Arithmetic Progression
Arithmetic Progression
A sequence where the difference between any two consecutive terms is constant.
Common Difference (d)
Common Difference (d)
The constant difference between consecutive terms in an arithmetic progression.
nth Term Formula
nth Term Formula
The formula used to find the nth term of an arithmetic progression, where a1 is the first term, d is the common difference, and n is the term number.
Arithmetic Series Sum
Arithmetic Series Sum
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Carl Friedrich Gauss
Carl Friedrich Gauss
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Study Notes
Arithmetic Progression (AP) Basics
- The nth term of an Arithmetic Progression can be calculated using the formula:
- nth term = a + (n - 1)d
- where 'a' is the first term, 'd' is the common difference, and 'n' is the term number.
Finding Specific Terms
- In the AP 2, 5, 8, 11, ..., to find which term equals 23:
- Use the nth term formula: 23 = 2 + (n - 1)3.
- Solving gives n = 8, meaning 23 is the 8th term.
Common Difference
- For the AP 10, 7, 4, 1, ..., the common difference 'd' can be identified:
- d = second term - first term = 7 - 10 = -3.
- This indicates a decreasing sequence.
Sum of the Series
- The sum of the arithmetic series 3, 6, 9, 12, ..., 99 can be calculated:
- First find the number of terms (n):
- Last term (99) = first term (3) + (n - 1) * common difference (3).
- Solve for n, yielding n = 33.
- Then use the formula for the sum:
- Sum = n/2 * (first term + last term), resulting in a total sum of 1683.
- First find the number of terms (n):
Historical Note
- The anecdote attributes the reinvention of methods to compute arithmetic progressions to prominent mathematicians, although the specific names may vary based on context.
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