Question

Which of these sequences is a geometric sequence? A. 1, 2, 4, 7, 11, 16, 22, … B. 2, 4, 8, 14, 22, 38, … C. 3, 6, 9, 12, 15, 18, 21, … D. 3, 9, 27, 81, 243, 729, …

Answer 1

Answer:

Ratio must be same .

D is the correct answer

Answer 2

(A) 1 , 2 , 4 , 7 , 11 , 16 , 22 ....

r = ²/₁ = ⁴/₂ ≠ ⁷/₄

Hence , not a GP or geometric sequence .

(B) 2 , 4 , 8 , 14 , 22 , 38 , ….

r = ⁴/₂ = ⁸/₄ ≠ ¹⁴/₈

Hence , not a GP .

(C) 3 , 6 , 9 , 12 , 15 , 21 , ....

r = ⁶/₃  ≠ ⁹/₆

Hence , not a GP .

(D) 3 , 9 , 27 , 81 , 243 , 729 ....

r = ⁹/₃ = ²⁷/₉ = ⁸¹/₂₇ = ²⁴³/₈₁ = ⁷²⁹/₂₄₃

Hence , a GP .