From the table given, Using the bacteria spores column,
a is the first term, r is the common ratio
We can deduce our first term, a is 2
The second term is 4 and the third term is 8 and n represents the number of terms,
Obviously, the sequence is not arithmetic but a geometric progression.
[tex]\begin{gathered} \text{first term, a=2} \\ \text{second term is 4} \\ \text{common ratio, r=}\frac{2^{nd}\text{ term}}{1^{st}\text{ term}}=\frac{4}{2}=2 \\ r=2 \end{gathered}[/tex]
Hence r = 2
Using the formula for a geometric progression,
[tex]U_n=ar^{n-1}[/tex][tex]\begin{gathered} \text{Where a=2 and r=2} \\ \text{Substitute the values of a and r into the above geometric formula} \\ U_n=2(2)^{n-1} \end{gathered}[/tex]
Hence, the explicit formula has been deduced above.
