Question

The sum of three consecutive numbers in G. P. is 35 and their product is 1,000. Find the numbers.​

Answer 1

Answer:

20, 10 and 5

Step-by-step explanation:

Let the numbers be a, ar and ar²

Sum =a+ ar + ar²=a(1+r+r² )=35……….(i)

Product =a× ar ×ar²=a³r³=1000

Hence ar=10 ➝a=10/r……….(ii)

Substitute a from (ii) in (i) gives

(10/r)(1+r+r²)=35

➝ 10+10r+10r²=35r

10r²-25r+10=0

2r²-5t+2=0

2r²-4r-r+2=0

2r(r-2)-(r-2)=0

(r-2)(2r-1)=0

Now either r-2=0 ➝r=2

or 2r-1=0 ➝r=1/2

When r=2 then a=10/r=10/2=5

Hence the numbers are 5, 10 and 20

When r=1/2 ➝ a=10/r=10/(1/2)=20

Hence the numbers are 20, 10 and 5.

Answer 2

Step-by-step explanation:

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