(d(1) = 3

(d(m) = d(n - 1) - 14
Find the 3*' term in the sequence.

1 answer

To solve the problem, we start with the given recurrence relation and the initial condition:

  1. \( d(1) = 3 \)
  2. \( d(m) = d(n - 1) - 14 \)

However, we need to clarify what the variables \( m \) and \( n \) stand for. It is reasonable to assume that we can express \( m \) in terms of \( n \), and suggest that \( m = n \).

Let's assume a pattern where \( m = n \). Hence, we can rewrite the recurrence as:

\[ d(n) = d(n - 1) - 14 \]

Now we can compute the subsequent terms of the sequence:

  • For \( n = 1 \): \[ d(1) = 3 \]

  • For \( n = 2 \): \[ d(2) = d(1) - 14 = 3 - 14 = -11 \]

  • For \( n = 3 \): \[ d(3) = d(2) - 14 = -11 - 14 = -25 \]

  • For \( n = 4 \): \[ d(4) = d(3) - 14 = -25 - 14 = -39 \]

Thus, the first four terms of the sequence are:

  • \( d(1) = 3 \)
  • \( d(2) = -11 \)
  • \( d(3) = -25 \)
  • \( d(4) = -39 \)

The third term, \( d(3) \), is:

\[ \boxed{-25} \]