Question

What is the 8th term of the following geometric sequence?
3, 15, 75, 375, …

Answer 1

`a_1=3\\a_2=3\cdot5=15\\a_3=15\cdot5=75\\a_4=75\cdot5=375\\\vdots\\\\\text{The general term of a geometric sequence}\ a_n=a_1r^(n-1)\\\\a_1-first\ term\\r-common\ ratio\\\\a_1=3,\ r=5\\\\\text{substitute}\\\\a_n=3(5^(n-1))\\\\8th\ term\to a_8\\\\\text{Substitute}\ n=8\ \text{to the equation of}\ a_n:\\\\a_8=3(5^(8-1))=3(5^7)=3(78125)=234,375\\\\Answer:\ 8th\ term=234,375`