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.Com
Question 259658: 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(32388) (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.
RELATED QUESTIONS
three numbers are in AP and their sum is 21. if 1,5,15 are added to them... (answered by Fombitz)
three numbers are in AP and their sum is 21. if 1,5,15 are added to them... (answered by Fombitz)
prove that if a series of numbers are in GP,their logarithms are in... (answered by Theo)
If the sums of the first three terms of an AP and a GP are equal and non-zero, the... (answered by greenestamps,ikleyn)
Three numbers are in AP such that their sum is 18 and sum of their squares is 158 the... (answered by ikleyn)
if three numbers are added in pairs the sum equal 10,19 and 21.find the... (answered by solver91311)
Question: The sum of three numbers in a GP is 14. If the first two terms are each... (answered by ikleyn)
The first, second and third term of a GP are the first, third and seventh term of an AP... (answered by greenestamps)
1. The sum of 4 integers is 24 and their product is 945. What are those integers?
2.... (answered by CPhill,greenestamps)