The first term of a G.P is 7. Find its 4th term, if its common ratio is 3.

Analyze the question You're given a geometric progression (G.P.) with first term a = 7 and common ratio r = 3. You need the 4th term.

Concept In a G.P., each term is the previous term multiplied by the common ratio. The nth term is:

Tₙ = a·rⁿ⁻¹

Solution For n = 4:

T₄ = 7 × 3⁴⁻¹ T₄ = 7 × 3³ T₄ = 7 × 27 T₄ = 189

Check by listing the terms:

• 1st term: 7
• 2nd term: 7 × 3 = 21
• 3rd term: 21 × 3 = 63
• 4th term: 63 × 3 = 189 ✓

Answer: C. 189

Tip: The power of r is always one less than the term number (n − 1). A common mistake is using 3⁴ = 81 and getting 7 × 81 = 567 (option A), which is the 5th term. Also, 63 (option D) is only the 3rd term, so count carefully!