Question

4) Find
\[c(3)\] in the sequence given by

\[\begin{cases}c(1)=20\\\\
c(n)=c(n-1)-17
\end{cases}\]
\[c(3)=\]

Answer 1

To find \( c(3) \) in the given sequence defined by

\[
\begin{cases}
c(1) = 20 \\
c(n) = c(n-1) - 17
\end{cases}
\]

we will calculate \( c(2) \) first and then \( c(3) \).

Starting with \( c(1) \):
\[
c(1) = 20
\]

Now we compute \( c(2) \):
\[
c(2) = c(1) - 17 = 20 - 17 = 3
\]

Next, we calculate \( c(3) \):
\[
c(3) = c(2) - 17 = 3 - 17 = -14
\]

Thus, the value of \( c(3) \) is

\[
\boxed{-14}
\]