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ICSE Class 10 Answered

Topic : GP Q5. The sum of 3 numbers is 63. If 2,7,21 are subtracted from these numbers in that order they form an AP. Find the numbers.
Asked by Pankaj | 07 Oct, 2018, 07:13: PM
answered-by-expert Expert Answer
Let the three numbers in the Geometric Series are a, ar, ar2.
given that a + ar + ar2 = 63
a = begin mathsize 16px style fraction numerator 63 over denominator 1 space plus space r space plus space r squared end fraction end style....(i)
According to the condition,
 
a - 2, ar - 7, ar2 - 21 forms an A.P.
Therefore (ar - 7) - (a - 2) = (ar2 - 21) - (ar - 7)
After solving, we get
 
a(r-1)2 = 9
Substitute the value of a from (i), we get
2r2 - 5r + 2 = 0  ....(use factorisation method)
r = 2 or r = 1/2
 
When r = 2 then a = 9..... from(i)
When r = 1/2 then a = 36..... from(i)
 
 
Wher r = 2 the three numbers in the geometric progression are 9, 18, 36 and

Wher r = 1/2 the three numbers in the geometric progression are 36, 18, 9
 
 


Answered by Yasmeen Khan | 08 Oct, 2018, 01:13: PM

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