Question

✠Mᴏᴅᴇʀᴀᴛᴇʀs
✠BrainlyStars ​

Topic - Geometric Progression

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If the sum and product of three numbers in GP are 31 and 125 respectively.

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Answer 1

Given:-

Sum=31

product=125

Step-by-step explanation:

Let the numbers be a/r,a,ar

here common ratio is same so they are in Gp

now a/r+a+ar=31

take r as LCM

a+ar+ar²/r=31

a+ar+ar²=31r------(1)

Now a×a/r×ar=125

a³=125

a=5

put value in eq (1)

5+5r+5r²=31r

5r²-26r+5=0

5r²-25r-r+5=0

5r(r-5)-1(r-5)=0

r=1/5. r=5

Therefore GP is

25,5,1

and

1,5,25

Answer 2

Answer:

hope it will help you to solve ur question