Question

write a recursive formula for (a_{n}), the (n^{th}) term of the sequence 7, - 35, 175, - 875, .... answer attempt 1 out of 2 (a_{1}=) (a_{n}=) submit answer (a_{n - 1})

Explanation:

Step1: Identify the first - term

The first term of the sequence \(7, - 35,175,-875,\cdots\) is \(7\), so \(a_1 = 7\).

Step2: Find the common ratio

To find the relationship between consecutive terms, divide the second term by the first term: \(\frac{-35}{7}=- 5\), divide the third term by the second term: \(\frac{175}{-35}=-5\), divide the fourth term by the third term: \(\frac{-875}{175}=-5\). The common ratio \(r=-5\).
For a recursive formula of a geometric sequence, \(a_n=r\times a_{n - 1}\). Here \(r = - 5\), so \(a_n=-5\times a_{n - 1}\).

Answer:

\(a_1 = 7\)
\(a_n=-5\times a_{n - 1}\)