{{ item.displayTitle }}
navigate_next
No history yet!
Progress & Statistics equalizer Progress expand_more
Student
navigate_next
Teacher
navigate_next
{{ filterOption.label }}
{{ item.displayTitle }}
{{ item.subject.displayTitle }}
arrow_forward
{{ searchError }}
search
{{ courseTrack.displayTitle }}
{{ printedBook.courseTrack.name }} {{ printedBook.name }}

# Writing and Using Explicit Rules for Geometric Sequences

## Writing and Using Explicit Rules for Geometric Sequences 1.13 - Solution

The first three elements in the geometric sequence are $a_1$, $a_2$ and $a_3$. We can determine them by substituting $1,\, 2$ and $3$ instead of $n$ in the formula $a_n = 3\cdot 5^{n-1}.$

$n$ $3\cdot 5^{n-1}$ $a_n$
${\color{#0000FF}{1}}$ $3\cdot 5^{{\color{#0000FF}{1}}-1}$ $3$
${\color{#0000FF}{2}}$ $3\cdot 5^{{\color{#0000FF}{2}}-1}$ $15$
${\color{#0000FF}{3}}$ $3\cdot 5^{{\color{#0000FF}{3}}-1}$ $75$

The sequence starts with $3$, $15$, and $75.$