The value of [tex]a_{5}[/tex] is 2500, when [tex]a_{1}=4[/tex] and [tex]5a_{n-1}[/tex].
Given that, [tex]a_{1}=4[/tex] and [tex]5a_{n-1}[/tex].
We need to find the value of [tex]a_{5}[/tex].
An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.
Now, to find the value of [tex]a_{5}[/tex] :
[tex]a_{2} =5a_{2-1}=5a_{1}=5 \times4=20[/tex]
[tex]a_{3} =5a_{3-1}=5a_{2}=5 \times20=100[/tex]
[tex]a_{4} =5a_{4-1}=5a_{3}=5 \times100=500[/tex]
[tex]a_{5} =5a_{5-1}=5a_{4}=5 \times500=2500[/tex]
Therefore, the value of [tex]a_{5}[/tex] is 2500.
To learn more about arithmetic sequence visit:
https://brainly.com/question/15412619.
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