How to answer these questions ?

Feb 24, 2018

$x = 15$ for an AP

$x = 9$ for a GP

Explanation:

a) For an AP, the difference between consecutive terms is equal we just need to find the average of the terms on either side,

$\frac{3 + 27}{2} = 15$

b) Since both $3$ (${3}^{1}$) and $27$ (${3}^{3}$) are powers of $3$, we can say that they form a geometric progression with a base of $3$ and a common ratio of $1$.

Therefore the missing term is simply ${3}^{2}$, which is $9$.