Respuesta :
The summation notion of given series is ∑50+5n , here n starts from 0 and the sum of given arithmetic series is 455.
The given arithmetic series is 50+55+60+ . . .
The summation notion of given series is ∑50+5n , here n starts from 0.
The sum of arithmetic series can be written as,
[tex]S_{n}[/tex] = [tex](n(a_{1} + a_{n}))/2[/tex]
n is the number of terms, [tex]a_{1}[/tex] is the first term and [tex]a_{n}[/tex] is the last term.
We have, n=7, [tex]a_{1}[/tex] = 50
To calculate sum of arithmetic series, we need to find [tex]a_{7}[/tex] .
[tex]a_{7} = a_{1} + (n-1)d[/tex]
d = 5 for the given series. On substituting value of n, [tex]a_{1}[/tex] and d in equation1, we get
[tex]a_{7}[/tex] = 50 + (7-1)(5)
[tex]a_{7}[/tex] = 50 + 30 = 80
On substituting values in sum of arithmetic series formula, we get
[tex]S_{7}[/tex] = (7(50 + (80)))/2 = 455
The summation notion of given series is ∑50+5n , here n starts from 0 and the sum of given arithmetic series is 455.
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