JEE Main 2014 Mathematics question on Sequences and Series
Three positive numbers form an increasing GP. If the middle term in this GP is doubled, then new numbers are in AP. Then, the common ratio of the GP is
A.
2+3
B.
3+2
C.
2−3
D.
2+3
Show answer and solution
Correct option: D
Solution
Let the three terms be a, ar, ar². Doubling the middle term gives a, 2ar, ar².
For AP: 2(2ar) = a + ar², so 4ar = a(1 + r²), giving r² - 4r + 1 = 0.
Solving: r = (4 ± √12)/2 = 2 ± √3. Since the GP is increasing with positive terms, r > 1, so r = 2 + √3.
[JEE Main 2014]
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