It is known exponentially that the first term is 2, the denominator is 3. Find the third term in this progression.

In this task, we will find a given member of a geometric progression;

For this, let us remember how a geometric progression is formed;

A geometric progression is a series of numbers, where each next is formed by multiplying the previous one by the denominator of the progression.

From the definition of progression we can find the third term;

b2 = 2 * 3 = 6;

b3 = 6 * 3 = 18 – the third term of the progression;

Or we can find any term by the formula;

bn = b1 * q ^ (n-1);

Let’s substitute our data into the formula and get;

b3 = 2 * 33-1 = 2 * 32 = 2 * 9 = 18.