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

Convert an arithmetic sequence between recursive and explicit form Precalculus

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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