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Between two numbers whose sum is 2, an even number of arithmetic means are inserted. If the sum of these means exceeds their number by unity, then the number of means are
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Correct option is A
Let 2n arithmetic means be A1, A2, A3, …, A2n between a and b. Then A1+A2+A3+…+A2n=a+b2×2n=1362×2n=13n6Given, A1+A2+A3+…+A2n=2n+1∴ 2n+1=13n6; or 12n+6=13n∴ n=6∴ The number of means =2n=2×6=12.Similar Questions
Between 1 and 31 are inserted M arithmetic means so that the ratio of the 7th and (M - 1) th means is 5:9, then the value of m is
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