Answer:
114688
Step-by-step explanation:
General form of a geometric sequence:
[tex]a_n=ar^{n-1}[/tex]
where:
- [tex]a_n[/tex] is the nth term
- a is the first term
- r is the common ratio
Given sequence: 7, 28, 112, ...
First term
From inspection of the given sequence, the first term is 7:
[tex]\implies a=7[/tex]
Common ratio
To find the common ratio r, divide consecutive terms:
[tex]\implies r=\dfrac{a_2}{a_1}=\dfrac{28}{7}=4[/tex]
Equation for the nth term
Substitute the found values of a and r into the formula to create an equation for the nth term:
[tex]\implies a_n=7(4)^{n-1}[/tex]
8th term
To find the 8th term, substitute n = 8 into the found equation:
[tex]\implies a_8=7(4)^{8-1}[/tex]
[tex]\implies a_8=7(4)^7[/tex]
[tex]\implies a_8=7(16384)[/tex]
[tex]\implies a_8=114688[/tex]
Learn more about geometric sequences here:
https://brainly.com/question/27783194
