Arithmetic and geometric sequence and series formulas for a high school Algebra 2 or precalculus course.
30 cards · basic cards · AI-written, checked twice. Edit anything.
- In an arithmetic sequence, what is the formula for the nth term?
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a_n = a_1 + (n-1)d- What does 'd' represent in an arithmetic sequence?
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The common difference (the constant amount added between consecutive terms)- In a geometric sequence, what is the formula for the nth term?
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a_n = a_1 * r^(n-1)- What does 'r' represent in a geometric sequence?
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The common ratio (the constant factor multiplied between consecutive terms)- What is the formula for the sum of a finite arithmetic series?
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S_n = n/2(a_1 + a_n) or S_n = n/2(2a_1 + (n-1)d)- What is the formula for the sum of a finite geometric series?
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S_n = a_1(1 - r^n)/(1 - r), provided r is not equal to 1- What is the formula for the sum of an infinite geometric series?
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S = a_1/(1 - r), provided the absolute value of r is less than 1- When does an infinite geometric series converge?
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When the absolute value of the common ratio is less than 1, or |r| < 1- What is the common difference of the sequence 5, 8, 11, 14, ...?
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3- What is the common ratio of the sequence 2, 6, 18, 54, ...?
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3- Find the 10th term of the arithmetic sequence with first term 3 and common difference 4.
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39- Find the 5th term of the geometric sequence with first term 2 and common ratio 3.
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162- What is the sum of the first 20 terms of the arithmetic sequence 1, 4, 7, 10, ...?
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590- What is the sum of the first 6 terms of the geometric sequence 1, 2, 4, 8, ...?
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63- Find the sum of the infinite geometric series 1 + 1/2 + 1/4 + 1/8 + ...
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