Complete the recursive formula of the arithmetic sequence 8,-5,-18,-31,dots d(1)= d(n)=d(n-1)+

Determining the Common Difference: To find the recursive formula for the arithmetic sequence, we need to determine the common difference between consecutive terms. We can do this by subtracting any term from the term that follows it. Calculation: -5 - 8 = -13 -18 - (-5) = -18 + 5 = -13 -31 - (-18) = -31 + 18 = -13 The common difference (d) is -13.Writing the Recursive Formula: Now that we have the common difference, we can write the recursive formula. The recursive formula for an arithmetic sequence is given by: d(n) = d(n-1) + d, where d(n) is the nth term and d is the common difference. Since the first term d(1) is 8, we can write the recursive formula as: d(1) = 8 d(n) = d(n-1) - 13 (since the common difference is -13)

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

8,-5,-18,-31,dots

d(1)=

d(n)=d(n-1)+

Complete the recursive formula of the arithmetic sequence $\newline$ $8,-5,-18,-31, \ldots \text {. }$ $\newline$ $d(1)=$ $\newline$ $d(n)=d(n-1)+$

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

8,-5,-18,-31, \ldots \text {. }

\newline

d(1)=

\newline

d(n)=d(n-1)+

Determining the Common Difference: To find the recursive formula for the arithmetic sequence, we need to determine the common difference between consecutive terms. We can do this by subtracting any term from the term that follows it. $\newline$ Calculation: $\newline$ $-5 - 8 = -13$ $\newline$ $-18 - (-5) = -18 + 5 = -13$ $\newline$ $-31 - (-18) = -31 + 18 = -13$ $\newline$ The common difference $d$ is $-13$ .
Writing the Recursive Formula: Now that we have the common difference, we can write the recursive formula. The recursive formula for an arithmetic sequence is given by: $\newline$ d(n) = d(n $-1$ ) + d, where d(n) is the $n$ th term and $d$ is the common difference. $\newline$ Since the first term $d(1)$ is $8$ , we can write the recursive formula as: $\newline$ $d(1) = 8$ $\newline$ $d(n) = d(n-1) - 13$ (since the common difference is $-13$ )