# SOLUTION: three numbers are in AP and their sum is 21. if 1,5,15 are added to them respectively,they form a GP.The numbers are. please tell me the solution and method of solving this type o

Algebra ->  Algebra  -> Sequences-and-series -> SOLUTION: three numbers are in AP and their sum is 21. if 1,5,15 are added to them respectively,they form a GP.The numbers are. please tell me the solution and method of solving this type o      Log On

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 Question 259657: three numbers are in AP and their sum is 21. if 1,5,15 are added to them respectively,they form a GP.The numbers are. please tell me the solution and method of solving this type of questions using this formula for Ap:(a-d),a, (a+d) and for GP:a/r,a,ar the option for the above question is :A)5,7,9 B)9,7,5 C) none of these the above is question of AP and GP. Answer by Fombitz(13828)   (Show Source): You can put this solution on YOUR website!Let A be your starting number, d be the difference for the arithmetic progression. Then from the geometric progression information, First: Second: Third: Since they are in geometric progression, each successive pair equals the common ratio. From eq. 1, you know, Substitute, Again using eq. 1, You can factor, Two solutions: . . . . . . A) (5,7,9) is one solution. But (23, 7, -9) is also a solution.