Answer to Question #273831 in Calculus for asmiro

Question

find the general term of the sequence, starting with n = 1. Determine whether the sequence converges and if so find its limit. If the sequence diverges, indicate that using the checkbox.

3, 3/19, 3/19^2, 3/19^3...

Answer 1

3, 3/19, 3/19^2, 3/19^3...

Given sequence is a GP whose first term $(a)$ is 3 and common ratio $(r)$ is 1/19.

$n^{th}$ term of a GP is given by: $a_n=a.r^{n-1}$

$a_n=\frac{3}{19^{n-1}}$

$\lim_{n\to\infty} a_n= \lim_{n\to\infty} \frac{3}{19^{n-1}}=0$