The explicit formula for given geometric sequence is:
[tex]a_n = 6 . 5^{n-1}[/tex]
Step-by-step explanation:
Given geometric sequence is:
6,30,150,750....
First of all we will find the common ratio.
Common ratio is the ratio between two consecutive terms of a geometric sequence
In the given sequence
a1 = 6
a2 = 30
a3 = 150
a4 = 750
Now
[tex]r=\frac{a_2}{a_1} = \frac{30}{6} = 5\\r=\frac{a_3}{a_2} = \frac{150}{30} = 5[/tex]
The explicit formula for geometric sequence is:
[tex]a_n = a_1 . r^{n-1}[/tex]
Putting the values of a1 and r
[tex]a_n = 6 . 5^{n-1}[/tex]
Keywords: Geometric sequence
Learn more about geometric sequence at:
#LearnwithBrainly
