1.3: Arithmetic progression and geometric progression

An arithmetic progression has a second term of $-14$ and a sum to 21 terms of 84. Find the first term and the 21st term of this progression.

A geometric progression has a second term of $27p^{2}$ and a fifth term of $p^{5}$. The common ratio, $r$, is such that $0 < r < 1$.

Find $r$ in terms of $p$.

Hence find, in terms of $p$, the sum to infinity of the progression.

Given that the sum to infinity is 81, find the value of $p$.