<p>The first three terms of a sequence are 3, −1, −1. The next terms are</p>
Step-by-Step Solution
Key Concept: Recognize the sequence as an Arithmetic-Geometric Progression (AGP) and use the given terms to find the parameters d and r.
<p><strong>Solution:</strong> The given sequence is not an AP or GP or HP. It is an AGP: $3, (3+d)r, (3+2d)r^2, ...$</p><p>From the given terms: $(3+d)r = -1$ and $(3+2d)r^2 = -1$</p><p>Eliminating r: $(3+d)^2 = -(3+2d)$</p><p>$\Rightarrow d^2 + 8d + 12 = 0 \Rightarrow d = -2, -6$</p><p>Then $r = -1, \frac{1}{3}$</p><p>Next term is $(3+3d)r^3 = 3$ or $-\frac{5}{9}$</p><p>∴ Correct answers are (b) and (d).</p>
Correct Answer: b, d