Algebra

Problems related to equations, functions, polynomials, etc.

Problems in this category

We are given that $S_n$ is the sum of the first $n$ terms of a sequence $\{a_n\}$. We are also given...

Sequences and SeriesArithmetic SequencesSummation

We are given a geometric sequence $\{a_n\}$ such that $a_5 = 1$ and $a_8 = 8$. We are asked to find ...

Geometric SequenceSequences and SeriesCommon Ratio

We are given an arithmetic sequence $\{a_n\}$. The sum of the first $n$ terms is denoted by $S_n$. ...

Arithmetic SequencesSeriesLinear EquationsCommon Difference

Given an arithmetic sequence $\{a_n\}$ and its sum of the first $n$ terms $S_n$. We are given that $...

Arithmetic SequenceSeriesSummation

Given an arithmetic sequence $\{a_n\}$, we know that $a_1 + a_7 = 42$. We are asked to find the sum ...

Arithmetic SequencesSeriesSummation

We are given a geometric sequence ${a_n}$ with the sum of the first $n$ terms denoted as $S_n$. We k...

Sequences and SeriesGeometric SequenceSum of Geometric Series

We are given an arithmetic sequence $\{a_n\}$ with the sum of the first $n$ terms denoted by $S_n$. ...

Arithmetic SequencesSeriesSummationCommon Difference

The problem states that ${a_n}$ is a geometric sequence, and $S_n$ represents the sum of the first $...

Sequences and SeriesGeometric SequenceSum of Terms

Given that the arithmetic mean of $m$ and $2n$ is 4, and the arithmetic mean of $2m$ and $n$ is 5, f...

Linear EquationsSystems of EquationsArithmetic MeanVariables

We are given an arithmetic sequence $\{a_n\}$ with $a_2 = 6$ and $a_6 = 18$. We need to find the sum...

Arithmetic SequencesSeriesSummation

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