Question

Write the first five terms of the geometric sequence defined recursively. Find the common ratio and write the $n^{th}$ term of the sequence as a function of $n$. (nth term formula: $a_n = a_1(r)^{n-1}$) $a_1 = 25$, $a_{k+1} = \frac{1}{5}a_k$ $a_1 = $ $a_2 = $ $a_3 = $ $a_4 = $ $a_5 = $

          Write the first five terms of the geometric sequence defined recursively. Find the common ratio and write the $n^{th}$ term of the sequence as a function of $n$.
(nth term formula: $a_n = a_1(r)^{n-1}$)
$a_1 = 25$, $a_{k+1} = \frac{1}{5}a_k$
$a_1 = $
$a_2 = $
$a_3 = $
$a_4 = $
$a_5 = $

Write the first five terms of the geometric sequence defined recursively. Find the common ratio and write the n^th term of the sequence as a function of n.
(nth term formula: an = a1(r)^n-1)
a1 = 25, ak+1 = (1)/(5)ak
a1 =
a2 =
a3 =
a4 =
a5 =

Added by Sonya R.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Gregory Higby

04/26/2023

Step 1

Given: a1 = 25, ak+1 = (1/5)ak a1 = 25 a2 = (1/5)a1 = (1/5)(25) = 5 a3 = (1/5)a2 = (1/5)(5) = 1 a4 = (1/5)a3 = (1/5)(1) = 1/5 a5 = (1/5)a4 = (1/5)(1/5) = 1/25 Show more…

Show all steps

Thanks for your feedback!

Write the first five terms of the geometric sequence defined recursively. Find the common ratio and write the n^(th ) term of the sequence as a function of n. (nth term formula: a_(n)=a_(1)(r)^(n-1) ) a_(1)=25,a_(k+1)=(1)/(5)a_(k) a_(1)= a_(2)= a_(3)= a_(4)= a_(5)= Write the first five terms of the geometric sequence defined recursively. Find the common ratio and write the nth term of the sequence as a function of n. (nth term formula: an = a1(r)n-1) 1 a1=25,ak+1= 5ak a1 a2 a3= a4= a5=