Question

find the 51st term of the arithmetic sequence 25, 12, -1, ...

Explanation:

Step1: Identify a₁ and d

In an arithmetic sequence, \( a_1 \) is the first term, and \( d \) is the common difference. Here, \( a_1 = 25 \). To find \( d \), subtract the first term from the second term: \( d = 12 - 25 = -13 \).

Step2: Use the nth term formula

The formula for the nth term of an arithmetic sequence is \( a_n = a_1 + (n - 1)d \). We need to find the 51st term, so \( n = 51 \). Substitute \( a_1 = 25 \), \( d = -13 \), and \( n = 51 \) into the formula:
\[

$$\begin{align*} a_{51} &= 25 + (51 - 1)(-13) \\ &= 25 + 50(-13) \\ &= 25 - 650 \\ &= -625 \end{align*}$$

\]

Answer:

\(-625\)