PCH Arithmetic and Geometric Serise and Sequences Formulas
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Last updated 2:49 PM on 5/16/23
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6 Terms
1
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Common Difference
d=(aₙ-a₁)/(n-1)
Change in # over change in n
Change in # over change in n
2
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Equation for Finding Nth term in an Arithmetic Sequence
aₙ=a₁+(n-1)d
3
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The equation for Finite Arithmetic Series (Finding the Sum of the first n Terms)
Sₙ=(n(a₁+aₙ))/2
4
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Equation for Finding Nth term in an Geometric Sequence
aₙ=a₁(rⁿ⁻¹)
5
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The equation for Finite Geometric Series (Finding the Sum of the first n Terms)
Sₙ= (a₁(1-rⁿ))/(1-r)
6
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The equation for infinite Geometric Series (Finding the Sum of ∞ Terms)
S∞=a₁/(1-r)
(called an Infinite Serise, and it is said to converge, or only exist if IrI<1)
(called an Infinite Serise, and it is said to converge, or only exist if IrI<1)