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compare and contrast geometric and arithmetic progressions.
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both geometric and arithmetic progressions are series of numbers that follow a certain pattern. in an arithmetic progression (ap), each term is found by adding a constant value to the previous term. on the other hand, in a geometric progression (gp), each term is found by multiplying the previous term by constant value. while an ap involves the addition of numbers, a gp involves the multiplication of numbers. additionally, the sum of terms in an ap over time will approach infinity, while the sum of terms in a gp will eventually settle at a fixed value.
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