31.6k views
4 votes
\[\begin{cases}c(1)=6\\\\ c(n)=c(n-1)-16 \end{cases}\]

User SuperCow
by
6.9k points

1 Answer

4 votes

Final answer:

The question involves a recursive function c(n) in Mathematics where each term is a sequence reduced by 16 from its preceding term. By using the initial condition c(1) = 6 and the recurrence relation, the sequence terms can be found for any positive integer n.

Step-by-step explanation:

The student has provided a recursive function, c(n), which defines a sequence where each term is derived by subtracting 16 from the previous term, starting with c(1) equal to 6.

The initial condition is given as c(1) = 6, and the recursive formula is c(n) = c(n-1) - 16.

To find the value of c(n) for any term n, you would use the recursive formula repeatedly, substituting n-1, n-2, etc., until you reach the initial condition.

Example Calculation:

Let's calculate c(4).

Start with the initial condition: c(1) = 6.

Using the recursive formula: c(2) = c(1) - 16 = 6 - 16 = -10.

Next term: c(3) = c(2) - 16 = -10 - 16 = -26.

Finally: c(4) = c(3) - 16 = -26 - 16 = -42.

This process can be continued for any positive integer value of n to determine the sequence values.

User Soupdiver
by
7.7k points