class 11

Math

Algebra

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 $4_{th}$ 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,2 1 $ 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