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  1. Home
  2. 12th grade
  3. Algebra I
  4. Exercise : Convert an arithmetic sequence between recursive and explicit form

Convert an arithmetic sequence between recursive and explicit form Algebra I

Find the explicit formula of the arithmetic sequences defined as follows. The first term of each sequence is a_1.

{\begin{cases} a_1=4 \cr \cr\forall n \in \mathbb{N}^*,\ a_{n+1}=a_n-2 \end{cases}\\}

\begin{cases} a_3=15 \cr \cr \forall n \in \mathbb{N}^*,\ a_{n+1}=a_n+4 \end{cases}\\

\begin{cases} a_1=-1 \cr \cr \forall n \geq2,\ a_{n+1}=a_{n-1}+6 \end{cases}\\

\begin{cases} a_1=-3 \cr \cr\forall n \in \mathbb{N}^*,\ a_{n+1}=a_n+5 \end{cases}\\

\begin{cases} a_1=0 \cr \cr\forall n \in \mathbb{N}^*,\ a_{n+2}=a_n-10 \end{cases}\\

\begin{cases} a_5=0 \cr \cr\forall n \in \mathbb{N}^*,\ a_{n+1}=a_n+5 \end{cases}\\

\begin{cases} a_1=-4 \cr \cr\forall n\geq2,\ a_{n+5}=a_{n-1}+18 \end{cases}\\

See also
  • Course : Sequences
  • Exercise : Determine whether a any sequence defined by a graph increases, decreases or is not monotonic
  • Exercise : Find the term of an arithmetic sequence
  • Exercise : Find the term of a geometric sequence
  • Exercise : Convert a geometric sequence between recursive and explicit form
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