Question 23 of 51intermediate🔧 ApplyShort Answer3 marks

Which term of the AP: 21, 18, 15, … is –81? Also, is 0 a term of this AP? Give reasons for your answer.

Correct Answer

(i) 35th term

(ii) Yes, 0 is a term of this AP because it occurs at the 8th position.

Exercise: Exercise Set 8.2 | Q: 2 | (Page 12)
For More Understanding

Explanation

The student needs to apply the nth term formula of an Arithmetic Progression, t_n = a + (n - 1)d, as illustrated in the textbook context. By substituting the given values for the first term (a) and common difference (d), the student solves for n. If n yields a positive integer, the term exists in the AP.

Solution Steps

  1. Step 1: Identify first term (a) = 21 and common difference (d) = 18 - 21 = -3.

  2. Step 2: For the first part, let t_n = -81. Using the formula t_n = a + (n - 1)d: -81 = 21 + (n - 1)(-3).

  3. Step 3: Solve for n: -81 - 21 = -3(n - 1) => -102 = -3(n - 1) => n - 1 = 34 => n = 35. So, -81 is the 35th term.

  4. Step 4: For the second part, let t_n = 0. Using the formula: 0 = 21 + (n - 1)(-3).

  5. Step 5: Solve for n: -21 = -3(n - 1) => n - 1 = 7 => n = 8. Since n is a positive integer, 0 is the 8th term of this AP.

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