Question 10 of 44intermediate🔧 ApplyShort Answer2 marks

Check whether -150 is a term of the AP: 11, 8, 5, 2 . . .

Correct Answer

No, -150 is not a term of the given AP.

Exercise: EXERCISE 5.2 | Q: 6 | (Page Page 14)
For More Understanding

Explanation

This question follows the same method as Example 6 in the textbook. To check if a number is a term of an AP, we use the nth term formula and solve for n. If n comes out to be a positive integer, the number is a term; otherwise, it is not.

Solution Steps

  1. Step 1: Identify the first term and common difference of the AP: a = 11, d = 8 - 11 = -3

  2. Step 2: Let -150 be the nth term. Using the formula aₙ = a + (n - 1)d, we get: -150 = 11 + (n - 1)(-3)

  3. Step 3: Solve for n: -150 = 11 - 3n + 3, which gives -150 = 14 - 3n

  4. Step 4: Simplifying: -164 = -3n, so n = 164/3

  5. Step 5: Since n = 164/3 is not a positive integer, -150 is not a term of the given AP.

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