Sequences and Series
Three positive numbers from an increasing G.P. If the middle term in this G.P. is doubled, the new numbers are in A.P. Then the common ratio of the G.P. is
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Prove that the sum of the n arithmetic means inserted between two quantities is n times the single arithmetic mean between them.
If 6 arithmetic means are inserted between 1 and 29, then find the 4th arithmetic mean.
There are n AM's between 1&31 such that 7th mean: (n−1)th mean =5:9, then find the value of n.
If a,b and c are positive real numbers then ba+cb+ac is greater than or equal to.
If A.M. between p and q (p≥ q) is two times the G.M. then p:q is.
Find x, if 2,x,21 are in G.P.
The AM between two positive numbers a and b(a>b) is twice their GM. Prove that a:b=(2+3):(2−3).
the arethmetic mean of two positive numbers a and b is twice their GM then a:b is