class 11

Math

Algebra

Sequences and Series

For any three positive real numbers $a,b$and $c,9(25a_{2}+b_{2})+25(c_{2}−3ac)=15b(3a+c)˙$Then :

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A.M. of $1,2,x,3$ is $0$, then $x=$ _____.

If the distinct points on the curve $y=2x_{4}+7x_{3}+3x−5$ are collinear, then find the arithmatic mean of x-coordinates of the aforesaid points

The minimum value of the sum of real numbers $a_{−5},a_{−4},3a_{−3},1,a_{8}$ and $a_{10}$ with $a>0$ 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.

the mean $xˉ$

Find the $3$ Arithmetic Means between $18$ and $30$