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أدلة الدراسة > College Algebra

Key Concepts & Glossary

Key Equations

recursive formula for nth term of an arithmetic sequence {a}_{n}={a}_{n - 1}+d\phantom{\rule{1}{0ex}}n\ge 2
explicit formula for nth term of an arithmetic sequence an=a1+d(n1)\begin{array}{l}{a}_{n}={a}_{1}+d\left(n - 1\right)\end{array}

Key Concepts

  • An arithmetic sequence is a sequence where the difference between any two consecutive terms is a constant.
  • The constant between two consecutive terms is called the common difference.
  • The common difference is the number added to any one term of an arithmetic sequence that generates the subsequent term.
  • The terms of an arithmetic sequence can be found by beginning with the initial term and adding the common difference repeatedly.
  • A recursive formula for an arithmetic sequence with common difference dd is given by an=an1+d,n2{a}_{n}={a}_{n - 1}+d,n\ge 2.
  • As with any recursive formula, the initial term of the sequence must be given.
  • An explicit formula for an arithmetic sequence with common difference dd is given by an=a1+d(n1){a}_{n}={a}_{1}+d\left(n - 1\right).
  • An explicit formula can be used to find the number of terms in a sequence.
  • In application problems, we sometimes alter the explicit formula slightly to an=a0+dn{a}_{n}={a}_{0}+dn.

Glossary

arithmetic sequence
a sequence in which the difference between any two consecutive terms is a constant
common difference
the difference between any two consecutive terms in an arithmetic sequence

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