CA Foundation · Quantitative Aptitude · Sequence and Series
For two distinct positive numbers a and b, the AM, GM and HM are A, G and H respectively. If A = 25 and H = 9, what is the value of G, and which relation holds among A, G, H?
G = 15 and A, G, H are in geometric progression. For two positive numbers G² = A×H = 25×9 = 225, so G = 15. The numbers 45 and 5 confirm this, with AM 25 and HM 9.
- AG = 15, and A, G, H are in GPCorrect
- BG = 17, and A, G, H are in AP
- CG = 15, and A, G, H are in HP
- DG = 16, and A, G, H are in GP
Explanation
G² = A×H = 225, so G = 15, and since G² = AH, A, G, H are in GP. Check: the numbers are 45 and 5 (sum 50, product 225); HM = 2×225/50 = 9. Option with HP is wrong because HP would need G = 2AH/(A+H), which is not 15.
Did you get it right without looking?
One question tells you little. A timed set on Sequence and Series shows your real accuracy, how long you take and where you lose marks.
More Sequence and Series questions
- Which of the following sequences is neither an arithmetic progression nor a geometric progression?
- The nth term of a sequence is given by Tn = 3n − 2 for odd n and Tn = n² for even n. What is the sum of the first six terms?
- How many terms of the AP 54, 51, 48, ... must be added to get a sum of 513?
- Meera invests ₹1,000 at the end of every year for 3 years in a scheme paying 10% p.a. compound interest. What is the accumulated value immed…
- A company's annual sales grow so that each year's increase is 10% of the previous year's sales. If sales in the first year are ₹2,00,000, wh…
- The sum of the first n terms of a series is given by Sn = 3n² + 2n for every n. What is the 10th term of the series?