Complete the recursive formula of the arithmetic sequence

Question

0,11,22,33, ....
c(1) =33.8 =___
c(n) = cn - 1) + ____

Answer 1

To complete the recursive formula for the given arithmetic sequence \(0, 11, 22, 33, \ldots\):

1. Finding \(c(1)\): In your sequence, the first term should be \(c(1) = 0\). The value \(33.8\) does not fit the sequence provided, so perhaps that was a typo or miscommunication.

2. Finding the common difference: The sequence increases by \(11\) each time (i.e., \(11 - 0 = 11\), \(22 - 11 = 11\), \(33 - 22 = 11\)). Therefore, the common difference \(d\) is \(11\).

3. Writing the recursive formula:

   • The first term can be represented as \(c(1) = 0\).
   • The recursive formula can be written as: \[ c(n) = c(n-1) + 11 \] for \(n > 1\).

So, the complete recursive formula for the arithmetic sequence is:

• \(c(1) = 0\)
• \(c(n) = c(n-1) + 11\) for \(n > 1\).