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How to solve a quartic equation given that the roots are all part of an arithmetic sequence?

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#arithmetic-progressions #quartics
64
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Defining a rigorous equation for the distance

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#arithmetic-progressions
84
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How do I solve the following exercise?

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#sequences-and-series #arithmetic-progressions #geometric-progressions
85
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Upper bound for recursion?

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#elementary-number-theory #inequality #arithmetic #recreational-mathematics #arithmetic-progressions
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$a, 1, b$ are three consecutive terms of an arithmetic series, find $a, b$ and $S$ of the infinite geometric series

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#sequences-and-series #arithmetic-progressions #geometric-series
56
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I am stuck on a question Algebra:Sequence and series, Can we make an infinitely long arithmetic progression from the set of prime integers?

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#sequences-and-series #arithmetic-progressions
110
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General formula for natural power summation

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#reference-request #proof-explanation #arithmetic-progressions
53
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How do I proceed with this?

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#arithmetic-progressions
147
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Find the total number of identical terms in 2 sequences.

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#sequences-and-series #arithmetic-progressions
82
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Is there generalization for gamma function?

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#gamma-function #arithmetic-progressions
90
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Confusion over terminology of arithmetic progression definition

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#sequences-and-series #arithmetic-progressions
114
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How do I derive a formula for summation of this series?

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#sequences-and-series #arithmetic-progressions #geometric-progressions
186
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If one Arithmetic Mean (A.M) $A$ and the two Geometric Means (G.M.'s) $G_1$ and $G_2$ are inserted between two given positive numbers, prove that:

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#sequences-and-series #arithmetic-progressions #geometric-progressions
104
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Length of Arithmetic Progressions Under Congruence Conditions

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#number-theory #modular-arithmetic #chinese-remainder-theorem #arithmetic-progressions
24.6k
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The Arithmetic Mean (A.M) between two numbers exceeds their Geometric Mean (G.M.)

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#sequences-and-series #algebra-precalculus #arithmetic-progressions #geometric-progressions

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