Question 15 of 44intermediate🔧 ApplyShort Answer3 marks

For what value of n, are the nth terms of two APs: 63, 65, 67, . . . and 3, 10, 17, . . . equal?

Correct Answer

n = 13

Exercise: EXERCISE 5.2 | Q: 15 | (Chapter: Page 14)
For More Understanding

Explanation

This question requires finding when the nth terms of two different APs are equal. The student needs to identify the first term and common difference of each AP, write the general formula for the nth term of each AP, equate them, and solve for n. The context provides the formula a_n = a + (n-1)d which is essential for solving this problem.

Solution Steps

  1. Step 1: For the first AP: 63, 65, 67, . . . — First term (a₁) = 63, Common difference (d₁) = 65 - 63 = 2

  2. Step 2: For the second AP: 3, 10, 17, . . . — First term (a₂) = 3, Common difference (d₂) = 10 - 3 = 7

  3. Step 3: Using the formula a_n = a + (n-1)d, write the nth term of first AP: 63 + (n-1)(2) = 63 + 2n - 2 = 61 + 2n

  4. Step 4: Write the nth term of second AP: 3 + (n-1)(7) = 3 + 7n - 7 = 7n - 4

  5. Step 5: Equate both nth terms: 61 + 2n = 7n - 4

  6. Step 6: Solve for n: 61 + 4 = 7n - 2n, which gives 65 = 5n, therefore n = 13

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