Write an explicit formula for a, start subscript, n, end subscript*an*​, the n, start superscript, th, end superscript*n*thterm of the sequence 2, comma, minus, 2, comma, minus, 6, comma, point, point, .2,−2,−6,....

The sequence given is: 2, -2, -6, ...

This suggests that the terms follow a linear pattern, where each term decreases by 4. To find an explicit formula for the \(n\)-th term, \(a_n\), of this sequence, let's break it down.

1. The first term \(a_1 = 2\).
2. The difference between consecutive terms is constant and equal to \(-4\).

This is an arithmetic sequence, and the general formula for the \(n\)-th term of an arithmetic sequence is:

\[
a_n = a_1 + (n-1) \cdot d
\]

Where:
- \(a_1 = 2\) (the first term),
- \(d = -4\) (the common difference),
- \(n\) is the term number.

Substituting the values for \(a_1\)

Write an explicit formula for a_n, the n-th term of the sequence 2, -2, -6, ....

Discover how to find the explicit formula for the arithmetic sequence 2, -2, -6... using the arithmetic sequence formula. Learn the step-by-step process for determining the common difference and deriving the general term. Suitable for students in Grades 6-8.

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