Question 32 of 44intermediate🔧 ApplyShort Answer3 marks

Find the sum of first 51 terms of an AP whose second and third terms are 14 and 18 respectively.

Correct Answer

The sum of first 51 terms is 5610.

Exercise: EXERCISE 5.3 | Q: 8 | (Page Page 21)
For More Understanding

Explanation

This question tests understanding of AP formulas for finding terms and sum. Students need to first find the common difference from consecutive terms, then find the first term, and finally apply the sum formula.

Solution Steps

  1. Step 1: Find the common difference (d): Since second term = 14 and third term = 18, we have d = 18 - 14 = 4

  2. Step 2: Find the first term (a): Using a₂ = a + d, we get 14 = a + 4, so a = 10

  3. Step 3: Apply the sum formula: S₅₁ = n/2[2a + (n-1)d] = 51/2[2(10) + 50(4)] = 51/2[20 + 200] = 51/2×2202 \times 220 = 51×11051 \times 110 = 5610

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