Complete the recursive formula of the arithmetic sequence {:[-1","-13","-25","-37","dots.],[a(1)=◻],[a(n)=a(n-1)+◻]:}

Identify first term: Identify the first term of the sequence. The first term of the sequence is given as -1. This will be our a(1) in the recursive formula.Determine common difference: Determine the common difference between consecutive terms. To find the common difference, subtract the first term from the second term: -13 - (-1) = -12. This is the common difference (d) for the arithmetic sequence.Write recursive formula: Write the recursive formula using the first term and the common difference. The recursive formula for an arithmetic sequence is a(n) = a(n-1) + d. Since we have a(1) = -1 and d = -12, the recursive formula becomes a(n) = a(n-1) - 12.Check formula with given terms: Check the recursive formula with the given terms to ensure it is correct. If we apply the formula a(n) = a(n-1) - 12 starting from the first term, we should get the subsequent terms of the sequence. For example, a(2) should be a(1) - 12, which is -1 - 12 = -13. This matches the second term of the sequence, so the formula appears to be correct.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Complete the recursive formula of the arithmetic sequence

{:[-1","-13","-25","-37","dots.],[a(1)=◻],[a(n)=a(n-1)+◻]:}

Complete the recursive formula of the arithmetic sequence $\newline$ $\begin{array}{l} -1,-13,-25,-37, \ldots . \\ a(1)=\square \\ a(n)=a(n-1)+\square \end{array}$

View step-by-step help

Home

Math Problems

Algebra 2

Write a formula for an arithmetic sequence

Full solution

Q. Complete the recursive formula of the arithmetic sequence

\newline

\begin{array}{l} -1,-13,-25,-37, \ldots . \\ a(1)=\square \\ a(n)=a(n-1)+\square \end{array}

Identify first term: Identify the first term of the sequence. The first term of the sequence is given as $-1$ . This will be our $a(1)$ in the recursive formula.
Determine common difference: Determine the common difference between consecutive terms. To find the common difference, subtract the first term from the second term: $-13 - (-1) = -12$ . This is the common difference $d$ for the arithmetic sequence.
Write recursive formula: Write the recursive formula using the first term and the common difference. The recursive formula for an arithmetic sequence is $a(n) = a(n-1) + d$ . Since we have $a(1) = -1$ and $d = -12$ , the recursive formula becomes $a(n) = a(n-1) - 12$ .
Check formula with given terms: Check the recursive formula with the given terms to ensure it is correct. If we apply the formula $a(n) = a(n-1) - 12$ starting from the first term, we should get the subsequent terms of the sequence. For example, $a(2)$ should be $a(1) - 12$ , which is $-1 - 12 = -13$ . This matches the second term of the sequence, so the formula appears to be correct.