Problem

Write a formula for the $n$th term of the arithmetic sequence $5,0,-5,-10,-15, \ldots$ The formula for the $n$th term of the sequence is $a_{n}=\square$.

Solution

Step 1 :Identify the common difference between the terms of the arithmetic sequence, which is \(-5\)

Step 2 :Determine the first term of the sequence, which is \(5\)

Step 3 :Use the formula for the \(n\)th term of an arithmetic sequence: \(a_{n} = a_{1} + (n-1)d\), where \(a_{1}\) is the first term and \(d\) is the common difference

Step 4 :Substitute the values of \(a_{1}\) and \(d\) into the formula: \(a_{n} = 5 + (n-1)(-5)\)

Step 5 :Simplify the formula to get the final answer: \(\boxed{a_{n} = 5 - 5(n-1)}\)

From Solvely APP
Source: https://solvelyapp.com/problems/GNcaXWEhA8/

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