To find the appropriate recursive formula for the given sequence \(5, -1, -7, -13, -19, \ldots\) where \( f(1) = 5 \) and \( n > 1 \), let's look at the differences between terms:
1. \( -1 - 5 = -6 \)
2. \( -7 - (-1) = -6 \)
3. \( -13 - (-7) = -6 \)
4. \( -19 - (-13) = -6 \)
The difference between consecutive terms is consistently \(-6\). Therefore, each term is obtained by subtracting 6 from the previous term. Translating this pattern into a recursive formula, we get:
\[ f(n + 1) = f(n) - 6 \]
Hence, the correct recursive formula is:
\[ f(n + 1) = f(n) - 6 \]
Which recursive formula can be used to generate the sequence shown, where f(1) = 5 and n > 1?
5,–1, –7, –13, –19, ...
f(n + 1) = f(n) + 6
f(n) = f(n +1) – 6
f(n +1) = f(n) – 6
f(n +1) = –6f(n)
1 answer
1 answer