<p>Find four numbers between 4 and 40 so that the six numbers are consecutive terms of an AP.</p>
Step-by-Step Solution
Key Concept: If six numbers form an AP with first term a₁ = 4 and last term a₆ = 40, use the AP formula aₙ = a₁ + (n-1)d to find the common difference, then generate all intermediate terms.
<p><strong>Step 1:</strong> Identify the structure. We need 6 consecutive AP terms: a₁ = 4, a₂ = ?, a₃ = ?, a₄ = ?, a₅ = ?, a₆ = 40</p><p><strong>Step 2:</strong> Use the formula for the nth term: aₙ = a₁ + (n-1)d</p><p>For the 6th term: a₆ = a₁ + 5d</p><p>40 = 4 + 5d</p><p>5d = 36</p><p>d = 36/5 = 7.2</p><p><strong>Step 3:</strong> Generate all six terms using d = 7.2:</p><p>• a₁ = 4</p><p>• a₂ = 4 + 7.2 = 11.2</p><p>• a₃ = 11.2 + 7.2 = 18.4</p><p>• a₄ = 18.4 + 7.2 = 25.6</p><p>• a₅ = 25.6 + 7.2 = 32.8</p><p>• a₆ = 32.8 + 7.2 = 40</p><p><strong>Step 4:</strong> The four numbers to be inserted between 4 and 40 are: <strong>11.2, 18.4, 25.6, 32.8</strong></p><p>∴ Answer: 11.2, 18.4, 25.6, 32.8 (or equivalently: 56/5, 92/5, 128/5, 164/5)</p>
Correct Answer: 11