Answer: 1, 2/3, 4/9,....
- A 1, 2/3, 4/9,...
- B 2, 4/3, 8/9,...
- C 3/2, 1, 2/3,...
- D 1, 1, 1,...
Correct answer: A. 1, 2/3, 4/9,...
Explanation: Let first term a, ratio r. Sum: a/(1-r)=3. Sum of squares: a²/(1-r²)=9/5. Dividing the second by the square of the first: (1-r)/(1+r) = (9/5)/9 = 1/5. So 5(1-r)=1+r, giving 4=6r, r=2/3. Then a=3(1-2/3)=1. Series: 1, 2/3, 4/9, ...
Bar heights for AP 2, 5, 8, 11 with the common difference d=3 marked between consecutive terms.
Concept context
Arithmetic progressions, geometric progressions, and sums