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alukav5142 [94]
2 years ago
5

What represents the recursive formula for the arithmetic sequence an=7-3(n-1)

Mathematics
1 answer:
Licemer1 [7]2 years ago
7 0

Answer:

\left\lbrace\begin{aligned}& a_{1} = 7 \\ & a_{n+1} = a_{n} - 3 && \text{for $n \ge 1$}\end{aligned}\right..

Step-by-step explanation:

An arithmetic sequence could be defined using only two pieces of information:

  • The first term of this sequence, a_{1}.
  • The common difference between two consecutive terms of this sequence, d.

The arithmetic sequence in this question is given in the explicit form, a_{n} = 7 - 3\, (n - 1), which is equivalent to a_{n} = 7 + (-3)\, (n - 1). In the explicit form, a_{1} and d are described in the same equation:

\text{$a_{n} = a_{1} + d\, (n - 1)$ for $n \ge 1$}.

Compare a_{n} = a_{1} + d\, (n - 1) with a_{n} = 7 + (-3)\, (n - 1): a_{1} = 7 whereas d = -3.

When an arithmetic sequence is given in the recursive form, a_{1} and d are specified in two separate equations:

\left\lbrace\begin{aligned}& a_{1} = a_{1} \\ & a_{n+1} = a_{n} + d && \text{for $n \ge 1$}\end{aligned}\right..

In this question, it was found that a_{1} = 7 whereas d = -3. Hence, the corresponding recursive formula for this arithmetic sequence would be:

\left\lbrace\begin{aligned}& a_{1} = 7 \\ & a_{n+1} = a_{n} + (-3) && \text{for $n \ge 1$}\end{aligned}\right..

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