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
detailed solution
Correct option is B
let A1, A2,.,. , Am be ,m arithmetic means between 1 and 31. ⇒Then A1,A2,…,Am31 is an AP with common difference.d=31−1m+1=30m+1 ∵d=b−an+1∴ A7=1+7d=1+7×30m+1=m+211m+1and Am−1=1+(m−1)d=1+30m+1(m−1)=31m−29m+1Now, A7Am−1=59m+21131m−29=59⇒ 9m+1899=155m−145⇒ 146m=2044⇒ m=14 (given)Similar Questions
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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