Question

An arithmetic sequence is given below.
25, 19, 13, 7, ...
Write an explicit formula for the nth term An

Answer 1

To find the explicit formula for the nth term \( A_n \) of the arithmetic sequence \( 25, 19, 13, 7, \ldots \), we first need to identify the first term and the common difference.

1. **First term** (\( A_1 \)):
- The first term \( A_1 = 25 \).

2. **Common difference** (\( d \)):
- The common difference can be found by subtracting the first term from the second term:
\[
d = A_2 - A_1 = 19 - 25 = -6
\]

Now that we have the first term and the common difference, we can use the formula for the nth term of an arithmetic sequence:
\[
A_n = A_1 + (n - 1) \cdot d
\]

Substituting the values we have:
\[
A_n = 25 + (n - 1)(-6)
\]

Now, simplify the formula:
\[
A_n = 25 - 6(n - 1)
\]
\[
A_n = 25 - 6n + 6
\]
\[
A_n = 31 - 6n
\]

Thus, the explicit formula for the nth term \( A_n \) is:
\[
A_n = 31 - 6n
\]