Question

If 2, 6, p, 54 and q are in continued proportion, find the values of p and q.

Answer 1

It is given that

$2,6,p,54$ and $q$ are in continued proportion

We can write it as

$2/6=6/p=p/54=54/q$

(i) We know that

$2/6=6/p$

By cross multiplication

$2p=36$

$p=18$

(ii) We know that

$p/54=54/q$

By cross multiplication

$pq=54\times 54$

Substituting the value of $p$

$q=(54\times 54)/18=162$

Therefore, the values of $p$ and $q$ are $18$ and $162.$