Question 13 of 44intermediate🔧 ApplyShort Answer2 marks

If the 3rd and the 9th terms of an AP are 4 and -8 respectively, which term of this AP is zero?

Correct Answer

Given that the 3rd term of an AP is 4 and the 9th term is -8. We need to find which term equals zero. Using the formula an=a+(n−1)da_n = a + (n-1)d, we have: a3=a+2d=4a_3 = a + 2d = 4 ... (1) and a9=a+8d=−8a_9 = a + 8d = -8 ... (2).

Subtracting (1) from (2): 6d=−126d = -12, so d=−2d = -2. Substituting in (1): a+2(−2)=4a + 2(-2) = 4, so a=8a = 8.

To find which term is zero: a+(n−1)d=0a + (n-1)d = 0. So 8+(n−1)(−2)=08 + (n-1)(-2) = 0, which gives 8−2n+2=08 - 2n + 2 = 0, so 10−2n=010 - 2n = 0, hence n=5n = 5. Therefore, the 5th term of this AP is zero.

Exercise: EXERCISE 5.2 | Q: 9 | (Page Page 14)
For More Understanding

Explanation

This question follows the same pattern as Example 4 in the textbook, where we find which term of an AP equals zero. The approach involves first finding the first term (a) and common difference (d) using the given terms, then setting the general term formula to zero to find n.

Solution Steps

  1. Step 1: Set up equations using nth term formula: a + 2d = 4 and a + 8d = -8

  2. Step 2: Subtract equations to get 6d = -12, hence d = -2

  3. Step 3: Substitute d = -2 in first equation to get a = 8

  4. Step 4: Set a + (n-1)d = 0 and solve: 8 + (n-1)(-2) = 0, giving n = 5

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