Question

an arithmetic sequence is given below.
25, 18, 11, 4, ...
write an explicit formula for the ( n^{\text{th}} ) term ( a_n ).
( a_n = )
(there is a math input keypad and some buttons for fraction and mixed number input)

Explanation:

Step1: Identify first term and common difference

For the arithmetic sequence \(25, 18, 11, 4, \dots\), the first term \(a_1 = 25\). The common difference \(d\) is \(18 - 25 = -7\) (or \(11 - 18 = -7\), etc.).

Step2: Use arithmetic sequence explicit formula

The explicit formula for the \(n\)-th term of an arithmetic sequence is \(a_n = a_1 + (n - 1)d\). Substituting \(a_1 = 25\) and \(d = -7\) into the formula:

$$
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$$

Answer:

\(a_n = 32 - 7n\)