document.write( "Question 1064171: A sequence of three real numbers forms an arithmetic progression with a first term of 9. If 2 is added to the second term and 20 is added to the third term, the three resulting numbers form a geometric progression. What is the smallest possible value for the third term of the geometric progression? \n" ); document.write( "

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A sequence of three real numbers forms an arithmetic progression with a first term of 9. If 2 is added to the second term and 20 is added to the third term, the three resulting numbers form a geometric progression. What is the smallest possible value for the third term of the geometric progression?
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Adding 2 to the 2nd term of the AP makes the GP’s 2nd term: 9 + d + 2, or 11 + d 
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document.write( "Adding 20 to the 3rd term of the AP makes the GP’s 3rd term: 9 + 2d + 20, or 29 + 2d\r
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document.write( "Since this is now a GP, the common ratio is calculated as:  =======> 
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document.write( " ------ Cross-multiplying
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document.write( "(d - 10)(d + 14) = 0 
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document.write( "d, or common difference = 10, or – 14\r
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document.write( "As the SMALLER 3rd term is being sought, we use d = - 14
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document.write( "Therefore, the SMALLER 3rd term of the GP =  \n" );
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