The common factors of 32 and 48 are 1, 2, 4, 8 and 16.
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The use of the expression 'common ratio' means that the sequence is a Geometric series where the terms are of the form a, ar ar2, ar3, ...arn-1 where a is the first term and r is the common ratio. The third term, a3 = 3 x 32 = 3 x 9 = 27
ar
In a geometric sequence where the terms always increase, the common ratio ( r ) must be greater than 1. This means that each term is obtained by multiplying the previous term by this positive ratio. For example, if the first term is ( a ) and the common ratio is ( r ), the sequence would look like ( a, ar, ar^2, ar^3, \ldots ) with each term growing larger than the last. Thus, the sequence exhibits exponential growth as long as the common ratio remains above 1.
a, ar, ar^2 and ar^3 where a and r are constants.
( a + ar ) = a ( 1 + r )