Question

an arithmetic sequence is given below.
-4, -1, 2, 5, ...
write an explicit formula for the n^th term a_n.

a_n =

Explanation:

Step1: Identify first term and common difference

For an arithmetic sequence, the first term \( a_1 = -4 \). The common difference \( d \) is found by subtracting consecutive terms: \( -1 - (-4) = 3 \), \( 2 - (-1) = 3 \), \( 5 - 2 = 3 \), so \( d = 3 \).

Step2: Use arithmetic sequence formula

The explicit formula for the \( n \)-th term of an arithmetic sequence is \( a_n = a_1 + (n - 1)d \). Substitute \( a_1 = -4 \) and \( d = 3 \):

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Answer:

\( a_n = 3n - 7 \)