Respuesta :
The summation notion of given series is ∑6+1.4n , here n starts from 0 and the sum of given arithmetic series is 143.
The given arithmetic series is 6+7.4+8.8+ . . .
The summation notion of given series is ∑6+1.4n , 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=11, [tex]a_{1}[/tex] = 6
To calculate sum of arithmetic series, we need to find [tex]a_{11}[/tex] .
[tex]a_{11} = a_{1} + (n-1)d[/tex]
d = 1.4 for the given series. On substituting value of n, [tex]a_{1}[/tex] and d in equation1, we get
[tex]a_{11}[/tex] = 6 + (11-1)(1.4)
[tex]a_{11}[/tex] = 6 + 14 = 20
On substituting values in sum of arithmetic series formula, we get
[tex]S_{7}[/tex] = (11(6 + 20))/2 = 143
The summation notion of given series is ∑6+1.4n , here n starts from 0 and the sum of given arithmetic series is 143.
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