Question

question write a recursive formula for $a_n$, the $n^{th}$ term of the sequence 1, 6, 11, 16, .... answer attempt 1 out of 2 $a_1=square$ $a_n=square$ submit answer $a_{n - 1}$

Explanation:

Step1: Identify the first - term

The first term of the sequence \(1,6,11,16,\cdots\) is \(1\), so \(a_1 = 1\).

Step2: Find the common difference

Subtract the first term from the second term: \(6 - 1=5\). Check with other consecutive terms, \(11 - 6 = 5\), \(16 - 11=5\). The common difference \(d = 5\).

Step3: Write the recursive formula

For an arithmetic sequence, the recursive formula is \(a_n=a_{n - 1}+d\). Since \(d = 5\), the formula is \(a_n=a_{n - 1}+5\).

Answer:

\(a_1 = 1\)
\(a_n=a_{n - 1}+5\)