Which term of AP \(53,48,43,\ldots\) is the first negative term?
12th
Step 1: Recall the formula for the \(n^{th}\) term of an Arithmetic Progression (AP):
\(a_n = a + (n - 1)d\)
Step 2: We want the first term that is negative, i.e., \(a_n < 0\).
So, \(53 + (n - 1)(-5) < 0\).
Step 3: Simplify the inequality:
\(53 - 5(n - 1) < 0\)
\(53 - 5n + 5 < 0\)
\(58 - 5n < 0\)
Step 4: Solve for \(n\):
\(58 < 5n\)
\(n > \dfrac{58}{5}\)
\(n > 11.6\)
Step 5: Since \(n\) must be a whole number (term number), the smallest integer greater than 11.6 is \(12\).
Therefore, the 12th term is the first negative term.