The sum of the first $16$ terms of the $AP: 10, 6, 2, \ldots$ is

Prove that $(a-b)^{2}, (a^{2}+b^{2})$ and $(a+b)^{2}$ form an $A.P.$

The ratio of the $11^{\text{th}}$ term to the $18^{\text{th}}$ term of an $AP$ is $2:3$. Find the ratio of the $5^{\text{th}}$ term to the $21^{\text{st}}$ term,and also the ratio of the sum of the first five terms to the sum of the first $21$ terms.

The taxi fare after each $km$,when the fare is $Rs. 15$ for the first $km$ and $Rs. 8$ for each additional $km$,does not form an $AP$ as the total fare (in $Rs.$) after each $km$ is $15, 8, 8, 8, \ldots$. Is the statement true? Give reasons.

The $21^{\text{st}}$ term of the $AP$ whose first two terms are $-3$ and $4$ is

For an $A.P.$,$T_{n} = \ldots \ldots \ldots \ldots (n > 1)$