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The product of 6 geometric means between 8 and 1/16 will be

The product of 6 geometric means between 8 and 1/16 will be

Grade:11

1 Answers

Arun
25750 Points
6 years ago
Dear Avinash
If there are 6 geometric means between 8 and 1/16
Then it means total 8 terms are present.
Hence
1/16 = 8 * r(8-1)
1/128 = r^7
(1/2)^7 = r^7
Hence r = 1/2.
Now 1st g.m. = a*r
2nd g.m. = ar²
So on...6th g.m = ar^6
Now
Product of these g.m will be = 
= ar * ar²* ar³ *ar⁴ *ar5 * ar6
 = a6 * r²¹
= 8 *(1/2)²¹
= (1/2)18
 
Regards
Arun (askIITians forum expert)

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