Question

question write a recursive formula for $a_n$, the $n^{th}$ term of the sequence 36, -6, 1, .... answer attempt 1 out of 2 $a_1=square$ $a_n=square$ $a_{n - 1}$ submit answer

Explanation:

Step1: Identify the first - term

The first term of the sequence \(36, - 6,1,\cdots\) is \(36\), so \(a_1 = 36\).

Step2: Find the common ratio

To find the common ratio \(r\) of a geometric sequence, we divide the second - term by the first - term. \(r=\frac{-6}{36}=-\frac{1}{6}\). In a geometric sequence, the recursive formula is \(a_n=r\times a_{n - 1}\). Since \(r =-\frac{1}{6}\), the formula for \(n\gt1\) is \(a_n=-\frac{1}{6}a_{n - 1}\).

Answer:

\(a_1 = 36\)
\(a_n=-\frac{1}{6}a_{n - 1},n\gt1\)