<p>The third term of a GP is 4. Then the product of the first 5 terms is</p>
Step-by-Step Solution
Key Concept: In a GP with first term 'a' and common ratio 'r', the product of terms equidistant from ends equals the square of the middle term. For 5 terms, the middle term (3rd term) appears once, and the product of all 5 terms = (middle term)^5.
<p><strong>Step 1:</strong> For a GP with 5 terms: a₁, a₂, a₃, a₄, a₅</p><p><strong>Step 2:</strong> The middle term (3rd term) is a₃ = ar² = 4</p><p><strong>Step 3:</strong> Product P = a₁ · a₂ · a₃ · a₄ · a₅ = a · ar · ar² · ar³ · ar⁴ = a⁵r¹⁰ = (ar²)⁵</p><p><strong>Step 4:</strong> Since ar² = 4, we have P = 4⁵ = 1024</p><p>∴ Answer: <strong>1024</strong> (Option B)</p>
Correct Answer: B