Question

You created a blog and after 2 weeks you get your first subscriber. The number of subscribers grows quickly, tripling each week afterwards. Excited about your blog's popularity you wonder, how many subscribers will the blog have 20 weeks after you created it?

Answer 1

From the information provided, we know that the first subscriber came after two weeks. This means as at the 20th week, your blog would have been growing for 18 weeks. Also take note that the first term in this sequence is 1, and the common ratio is 3. We know this because the number of subscribers triples each week after the first subscriber.

Therefore, for the geometric sequence, we have the following;

$\begin{gathered} a_1=1 \\ r=3 \\ \end{gathered}$

The nth term of a geometric progression is given as;

$a_n=ar^{n-1}$

For the 18th term, which is the number of subscribers after the 20th week, we would have;

$\begin{gathered} a_{18}=a\times r^{18-1} \\ a_{18}=1\times3^{17} \\ a_{18}=129,140,163 \end{gathered}$

ANSWER:

This means 20 weeks after the blog was created, you now have

129,140,163 subscribers