Respuesta :
Answer: 4865
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Explanation:
The sequence {3,11,19,...} is arithmetic since we are adding 8 to each term to get the next one
- 3+8 = 11
- 11+8 = 19
etc. This means the common difference is d = 8.
The first term is a = 3
Let's use this formula
S = n*(2*a + d(n - 1) )/2
so we can find the sum of the first n terms. In this case, n = 35
So,
S = n*(2*a + d(n - 1) )/2
S = 35*(2*3 + 8(35 - 1) )/2
S = 35*(6 + 8(34))/2
S = 35*(6 + 272)/2
S = 35*(278)/2
S = 35*139
S = 4865
[tex]4865[/tex] is the the sum of the first [tex]35[/tex] terms of the following series [tex]3, 11, 19...[/tex]
What is arithmetic sequence?
An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant. For instance, the sequence 5, 7, 9, 11, 13, 15.. . is an arithmetic progression with a common difference of 2
The sequence [tex]{3,11,19,...}[/tex] is arithmetic since we are adding [tex]8[/tex] to each term to get the next one as shown below:
[tex]3+8 = 11\\11+8 = 19[/tex]
This means the common difference is [tex]d = 8.[/tex]
The first term is [tex]a = 3[/tex]
Number of terms [tex]=n=35[/tex]
Sum of the series
[tex]=\frac{n}{2} (2a+(n-1)d)[/tex]
[tex]=\frac{35}{2} (2[/tex]×[tex]3+34[/tex]×[tex]8)[/tex]
[tex]=35[/tex]×[tex]139[/tex]
[tex]=4865[/tex]
Hence, we can conclude that the sum of the first [tex]35[/tex] terms of the following series is [tex]4865[/tex]
Learn more about arithmetic sequence here:
https://brainly.com/question/27079755?referrer=searchResults
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