Question

Write a recursive formula for a, start subscript, n, end subscripta
n
​
, the n, start superscript, th, end superscriptn
th
term of the sequence 18, comma, 25, comma, 32, comma, 39, comma, dot dot dot18,25,32,39,....
Answer
Attempt 1 out of 2

a, start subscript, 1, end subscript, equalsa
1
​
=

a, start subscript, n, end subscript, equalsa
n
​
=

Answer 1

To develop a recursive formula for the sequence given (18, 25, 32, 39, ...), we first need to analyze how the sequence progresses between the terms.

1. **Identify the pattern**:
- The differences between consecutive terms are:
- 25 - 18 = 7
- 32 - 25 = 7
- 39 - 32 = 7
- It's clear that each term increases by 7.

2. **Recursive formula**:
- The first term of the sequence can be identified as \( a_1 = 18 \).
- The relationship between consecutive terms can be described as:
- \( a_n = a_{n-1} + 7 \) for \( n \geq 2 \).

Thus, the recursive formula for the sequence can be summarized as:

\[
\begin{align*}
a_1 & = 18, \\
a_n & = a_{n-1} + 7 \quad \text{for } n \geq 2.
\end{align*}
\]