Question

vv5) Here is the general recursive formula for arithmetic sequences.

\[\begin{cases}g(1)=A\\\\
g(n)=g(n-1)+B
\end{cases}\]
What is the common difference of the sequence?
Choose 1 answer:
Choose 1 answer:
(Choice A)
\[A\]
A
\[A\]
(Choice B)
\[B\]
B
\[B\]
(Choice C)
\[A+B\]
C
\[A+B\]
(Choice D)
\[B-A\]
D
\[B-A\]

Answer 1

The common difference of an arithmetic sequence is the value that is added to each term to get to the next term. According to the general recursive formula given:

\[
\begin{cases}
g(1) = A \\
g(n) = g(n-1) + B
\end{cases}
\]

the term \(g(n)\) is obtained from the previous term \(g(n-1)\) by adding \(B\). Therefore, the common difference of the sequence is \(B\).

Thus, the correct answer is:

(Choice B)
\[B\]