Progression (Sequence and Series)Hard
Question
If x1, x2, x3 as well as y1, y2, y3 are in GP with the same common ratio, then the points (x1, y1), (x2, y2) and (x3, y3)
Options
A.lie on a straght line
B.lie on an ellipse
C.lie on a circle
D.are vertice of a triangle
Solution
Let 
and 
⇒ x2 = x1r, x3 = x1r3 y2 = y1r and y3 = y1r2
Again, ᐃ =
Applying R2 → R2 - rR1 and R3 → R3 - rR2
(∵ R2 and R3 are identical)
Hence, (x1, y1), (x2, y2), (x3, y3) lie on a straight line.
and ⇒ x2 = x1r, x3 = x1r3 y2 = y1r and y3 = y1r2
Again, ᐃ =
Applying R2 → R2 - rR1 and R3 → R3 - rR2
(∵ R2 and R3 are identical)Hence, (x1, y1), (x2, y2), (x3, y3) lie on a straight line.
Create a free account to view solution
View Solution FreeMore Progression (Sequence and Series) Questions
Let f(x) be a polynomial function of second degree. If f(1) = f(-1) and a, b, c are in A. P., then f′(a), f′...If 100 times the 100th term of an A.P. with non-zero common difference equals the 50 times its 50th term, then the 150th...If = 2(3n − 1) V n ≥ 1, then is equal to -...Let a1, a2, a3,..... be in harmonic progression with a1 = 5 and a20 = 25. The least positive integer n forwhich an...The sum of first 9 terms of the series + .... is....