The sum of three terms of an Arithmetic Progression $(AP)$ is $18$ and the sum of their squares is $158$. The largest term is.......

Given an $A.P.$ whose terms are all positive integers. The sum of its first nine terms is greater than $200$ and less than $220$. If the second term is $12$,then its $4^{th}$ term is:

Jairam purchased a house for Rs. $15000$ and paid Rs. $5000$ at once. He promised to pay the remaining amount in annual installments of Rs. $1000$ with $10\%$ per annum interest on the outstanding balance. How much total money will be paid by Jairam in Rs.?

There are $n$ arithmetic means between $7$ and $71$. If the $5^{th}$ arithmetic mean is $27$,then $n = ......$

Between $1$ and $31$,$m$ numbers have been inserted in such a way that the resulting sequence is an $A.P.$ and the ratio of the $7^{\text{th}}$ and $(m-1)^{\text{th}}$ inserted numbers is $5:9$. Find the value of $m$.

Let $x, y, z$ be positive real numbers such that $x + y + z = 12$ and $x^3y^4z^5 = (0.1)(600)^3$. Then $x^3 + y^3 + z^3$ is equal to