Write the sum using summation notation, assuming the suggested pattern continues. 8  40 + 200  1000 + ...
Mathematics
Garfield10
Question
Write the sum using summation notation, assuming the suggested pattern continues. 8  40 + 200  1000 + ...
2 Answer

1. User Answers LammettHash
Each successive term is 5 times the previous one, so the underlying sequence is
[tex]a_n=5a_{n1}=(5)^2a_{n2}=(5)^3a_{n3}=\cdots=(5)^{n1}a_1=8(5)^{n1}[/tex]
The sum can then be written as
[tex]840+2001000+\cdots=\displaystyle\sum_{n=1}^\infty8(5)^{n1}[/tex] 
2. User Answers boffeemadrid
Answer:
Stepbystep explanation:
From the given information, the pattern is as:
8  40 + 200  1000 + ...
We can see that the successive term is 5 times the previous one, therefore, using this, we can write it in the form of sequence:
[tex]a_{n}=5a_{n1}=(5)^2a_{n2}=(5)^3a_{n3}=....=(5)^{n1}a_{1}=8(5)^{n1}[/tex].
Therefore, the sum can be written as:
8  40 + 200  1000 + ...=[tex]\sum_{n=1}^{\infty}8(5)^{n1}[/tex]