Given the first three terms of a geometric sequence:
[tex]\text{ 4, 20, 100}\ldots[/tex]To be able to determine the next 2 terms, let's first find out their common ratio r.
[tex]\begin{gathered} \text{ }\frac{20}{4}\text{ = 5} \\ \\ \frac{100}{20}\text{ = 5} \end{gathered}[/tex]Therefore, the common ratio r is 5.
Let's find the next 2 terms:
a.) The 4th term.
[tex]\text{ A}_4=A_1(r)^{n\text{ - 1}}=(4)(5)^{4\text{ - 1}}=(4)(5)^3[/tex][tex]\text{ = (4)(125)}[/tex][tex]\text{ A}_4\text{ = 500}[/tex]b.) The 5th term.
[tex]\text{ A}_4=A_1(r)^{n\text{ - 1}}=(4)(5)^{5\text{ - 1}}=(4)(5)^4[/tex][tex]\text{ = 4(625)}[/tex][tex]\text{ A}_5\text{ = 2,500}[/tex]Therefore, the next 2 terms (4th and 5th) of the geometric sequence are 500 and 2,500 respectively.
