Arithmetic Sequences and Series: Key Concepts
Master the formulas, vocabulary, and techniques for working with arithmetic sequences and their sums.
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Questions Covered in This Set
8 cards to master
What is the common difference (d) in an arithmetic sequence?
The constant amount by which each term differs from the previous term in the sequence.
What is the nth term formula for an arithmetic sequence?
aₙ = a₁ + (n - 1)d, where aₙ is the nth term, a₁ is the first term, n is the position, and d is the common difference.
What is an arithmetic series?
The sum of the terms in an arithmetic sequence.
What is the formula for the sum of the first n terms of an arithmetic series?
Sₙ = n(a₁ + aₙ)/2 or Sₙ = n[2a₁ + (n - 1)d]/2
In the sequence 3, 7, 11, 15, ..., what is the common difference?
d = 4, since each term increases by 4 from the previous term.
How did Gauss calculate the sum 1 + 2 + 3 + ... + 100?
He paired terms (1+100, 2+99, etc.) to get 100 pairs of 101, then calculated 100(101)/2 = 5,050.
If a₁ = 5, d = 3, and n = 12, what is a₁₂?
a₁₂ = 5 + (12-1)(3) = 5 + 33 = 38
What information do you need to find any term in an arithmetic sequence?
The first term (a₁), the common difference (d), and the position (n) of the term you want to find.
