These are sample practice MCQs created for exam preparation. These are NOT official exam questions.
In a sequence, each term after the first is k times the previous term. What is the value of the 4th term? (1) The first term is 3 (2) The ratio of the 3rd term to the 2nd term is 2
Question:
In a sequence, each term after the first is k times the previous term. What is the value of the 4th term? (1) The first term is 3 (2) The ratio of the 3rd term to the 2nd term is 2
In a sequence, each term after the first is k times the previous term. What is the value of the 4th term? (1) The first term is 3 (2) The ratio of the 3rd term to the 2nd term is 2
Options
Answer: (C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
Explanation:
Geometric sequence: aₙ = a₁ × k^(n-1). Statement (1): a₁ = 3, but k unknown. Cannot find a₄ = 3k³. Insufficient. Statement (2): a₃/a₂ = k = 2, but a₁ unknown. Cannot find a₄. Insufficient. Together: a₁ = 3, k = 2. Therefore a₄ = 3 × 2³ = 3 × 8 = 24. Sufficient.
Explanation:
Geometric sequence: aₙ = a₁ × k^(n-1). Statement (1): a₁ = 3, but k unknown. Cannot find a₄ = 3k³. Insufficient. Statement (2): a₃/a₂ = k = 2, but a₁ unknown. Cannot find a₄. Insufficient. Together: a₁ = 3, k = 2. Therefore a₄ = 3 × 2³ = 3 × 8 = 24. Sufficient.
👉 Want AI explanation? Open in MCQ App
Recommended articles
- How To Cover Current Affairs For Upsc Prelims — Master UPSC Current Affairs with daily newspaper reading, Vision IAS monthly compilations, PT 365, and MCQ practice. Complete strategy guide for Prelims…
- Top 10 Daily Current Affairs Resources For Upsc Aspirants — Discover the best daily current affairs resources for UPSC 2026. Complete guide with The Hindu, PIB, Sansad TV, and 7 more proven sources. Expert…
- Free Cat Previous Year Questions Guide — Master CAT 2025 with free previous year questions. Practice 1000+ PYQs, mock tests, and detailed solutions. Complete guide to CAT preparation using past…