Algebra 2 Final Exam Formula – Flashcards
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To find the sum of a certain number of terms of an arithmetic sequence:
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Sn=[n(a₁+an)]/2
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To find any term of an arithmetic sequence:
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an = a₁ + (n - 1)d d=common difference
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Find the 10th term of the sequence 3, 5, 7, 9, ...
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n = 10; a1 = 3, d = 2 an = a₁ + ( n - 1 ) d a₁₀ = 3+(10 - 1) 2 a₁₀ = 21 The tenth term is 21.
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A theater has 60 seats in the first row, 68 seats in the second row, 76 seats in the third row, and so on in the same increasing pattern. If the theater has 20 rows of seats, how many seats are in the theater?
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The seating pattern is forming an arithmetic sequence. 60, 68, 76, ... We wish to find "the sum" of all of the seats. n = 20, a1 = 60, d = 8 and we need a20 for the sum. an = a₁ + ( n - 1 )d a²⁰ = 60 + (20-1)8 a₂₀ = 212 Now, use the sum formula: Sn = [ n( a₁ + an ) ]/2 S₂₀ = 20(60+212)/2 =2720 There are 2720 seats.
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Arithmetic mean
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[x + y] / 2
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Arithmetic Series
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Sn = n/2 (a₁ + an) Sn=sum n=term # a₁= 1st term an= nth term
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Geometric Sequence
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an = a₁r ⁿ⁻¹ an=nth term a₁=1st term r= common ratio n= term #
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Geometric Mean
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√xy
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Common ratio
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r = a₂/a₁
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Geometric Series Finite
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Sn = [a₁(1-r ⁿ)] / 1 - r
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Geometric Series Infinite
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Sn = (a₁) / 1 - r
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Summation notation
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× ∑ ( n - 1) ⁿ=×
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Ellipse ↔ horizontal
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x²/a² + y²/b² = 1 major axis : √a² × 2 minor axis : √b² × 2
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Ellipse | Vertical
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x²/b² + y²/a² = 1 major axis : √a² × 2 minor axis : √b² × 2
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Circle
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Center x²+y²=r²←radius (at origin) (x - h )²+ (y - k )²=r² (at (h,k))
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Circle: use to find the radius given the center and a point on the circle
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d=[√(x₁-x₂)²+(y₁−y₂)²]
