Do This Problem If You Are Truly Bored

We are asked to find the 20th term that occurs in the sequence $1234, 4936, 19744, 78976, 315904$ . Using the general formula for finding any number in a geometric progression, we can accomplish this. However, we need to first find the initial term and the common ratio between the numbers. The initial term is the number that the sequence starts with. In this case, the initial term is $1234$ . On the other hand, the common ratio is the factor at which each number is increasing. We can divide any two consecutive numbers to find this. $\frac{4936}{1234}=4$ Thus, the common ratio between the numbers is $4$ . Now that we've found all the necessary information needed to calculate the 20th term in the sequence, we can plug in all the values into the formula $a_n=a \times r^{n-1}$ . $\begin{aligned} a_{20}=(1234) \times (4)^{20-1} \implies \ a_{20}=(1234) \times (4)^{19}\implies \ a_{20}=1234 \times a_20=(1234) \times (4)^{19} \implies \ a_{20}=\boxed{339199337168896} \end{aligned}$