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Q. No 6Find three consecutive terms in an A. P. Whose sum is 27 and their product is 512.​

Answer»

ong>Answer:

LET the numbers be (a−d),a,(a+d). Then,

Sum=−3⇒(a−d)+a+(a+d)=−3⇒3a=−3⇒a=−1

Product of their cubes=512⇒(a−d)3×a3×(a+d)3=512

⇒(a2−d2)3×a3=512         

⇒−(1−d2)3=512            (∵a=−1)

⇒−(1−d2)=8            

⇒d2=9⇒d=±3    

If d=3, then the numbers are −4,−1,2. If d=−3, then the numbers are 2,−1,−4.


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