Complete the recursive formula of the geometric sequence 500,200,80,32,dots. c(1)= c(n)=c(n-1).

Identify first term: We are given the sequence 500, 200, 80, 32, ... First, we identify the first term of the sequence. The first term is 500.Find common ratio: Next, we need to find the common ratio by dividing the second term by the first term. The common ratio r is 200 / 500 = 0.4.Write recursive formula: Now we can write the recursive formula for the geometric sequence. The first term is given by c(1) = 500. For n > 1, the nth term is found by multiplying the previous term by the common ratio. So, c(n) = c(n-1) * 0.4.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Complete the recursive formula of the geometric sequence
500,200,80,32,dots.

c(1)=
c(n)=c(n-1).

Complete the recursive formula of the geometric sequence $\newline$ $500, 200, 80, 32, \dots$ . $\newline$ $c(1)=$ $\newline$ $c(n)=c(n-1)\cdot$

View step-by-step help

Home

Math Problems

Algebra 1

Write variable expressions for geometric sequences

Full solution

Q. Complete the recursive formula of the geometric sequence

\newline

500, 200, 80, 32, \dots

\newline

c(1)=

\newline

c(n)=c(n-1)\cdot

Identify first term: We are given the sequence $500$ , $200$ , $80$ , $32$ , ... $\newline$ First, we identify the first term of the sequence. $\newline$ The first term is $500$ .
Find common ratio: Next, we need to find the common ratio by dividing the second term by the first term. $\newline$ The common ratio $r$ is $\frac{200}{500} = 0.4$ .
Write recursive formula: Now we can write the recursive formula for the geometric sequence. $\newline$ The first term is given by $c(1) = 500$ . $\newline$ For n > 1, the $n$ th term is found by multiplying the previous term by the common ratio. $\newline$ So, $c(n) = c(n-1) \times 0.4$ .