Question 28 of 44intermediate🔧 ApplyShort Answer3 marks

How many terms of the AP: 9, 17, 25, . . . must be taken to give a sum of 636?

Correct Answer

12 terms must be taken to give a sum of 636.

Exercise: EXERCISE 5.3 | Q: 4 | (Page Page 21)
For More Understanding

Explanation

This is a direct application of the sum formula for an AP, similar to Example 13 in the textbook. The student must identify the first term and common difference from the given AP, substitute into the sum formula, and solve the resulting quadratic equation. Only the positive integer solution is valid for the number of terms.

Solution Steps

  1. Step 1: Identify the values: First term (a) = 9, Common difference (d) = 17 - 9 = 8, Sum (S_n) = 636

  2. Step 2: Apply the sum formula: S_n = n/2[2a + (n-1)d]

  3. Step 3: Substitute values: 636 = n/2[2(9) + (n-1)(8)]

  4. Step 4: Simplify: 636 = n/2[18 + 8n - 8] = n/2[8n + 10] = n(4n + 5)

  5. Step 5: Form quadratic equation: 4n² + 5n - 636 = 0

  6. Step 6: Solve using quadratic formula: n = (-5 ± 25+10176\sqrt{25 + 10176})/8 = (-5 ± 101)/8

  7. Step 7: Get solutions: n = 12 or n = -13.25. Since n must be positive, n = 12

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