NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 5: Arithematic Progressions - Exercise 5.3

Question 17

Step 1: Recall the formula for the \(n^{th}\) term of an Arithmetic Progression (AP):

\(a_n = a + (n - 1)d\)

• Here, \(a = 53\) (the first term).
• \(d = 48 - 53 = -5\) (the common difference).

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.