matematika



arithmetic progression

Arithmetic and Geometric progressions.
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arithmetic progression

Postby sarah » Mon Dec 07, 2009 2:44 am

The sum of 3 numbers in arithmetic progression is 45. If 2 is added to the first number, 3 to the second and 7 to the third, the new numbers will be in geometrical progression. Find the common difference in arithmetic progression.

What do you think is the answer? :P :P :P


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Re: arithmetic progression

Postby martin123456 » Tue Dec 08, 2009 4:09 pm

sarah wrote:The sum of 3 numbers in arithmetic progression is 45. If 2 is added to the first number, 3 to the second and 7 to the third, the new numbers will be in geometrical progression. Find the common difference in arithmetic progression.

What do you think is the answer? :P :P :P

let them be a, a+d, a+3d
=> a+a+d+a+2d=3(a+d)=45=>a+d=15
a+2,a+d+3,a+2d+7 is geometrical progression
a=15-d
=>
17-d, 18, 22+d is geom prog
=> 18^2=(17-d)(22+d)
solve this quadratic equation and find d
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