The given series is an illustration of an arithmetic series, where the sum of first 10 terms of the series is -160.
Given
[tex]2 + (-2) + (-6) + (-10) +.......[/tex]
First, we calculate the common difference of the series
[tex]d = T_2 - T_1[/tex]
[tex]d = -2 -2[/tex]
[tex]d = -4[/tex]
The sum of the first nth term of an arithmetic series is:
[tex]S_n = \frac n2(2a + (n - 1)d)[/tex]
Where:
[tex]n = 10[/tex] ---- i.e. sum of 10 terms
[tex]a = 2[/tex] --- the first term
[tex]d = -4[/tex] --- the common difference
So, we have:
[tex]S_{10} = \frac{10}{2}(2 \times 2 + (10 - 1) \times -4)[/tex]
[tex]S_{10} = 5(4 + 9 \times -4)[/tex]
[tex]S_{10} = 5(-32)[/tex]
[tex]S_{10} = -160[/tex]
Hence, the sum of 10 terms of the series is -160.
Read more about arithmetic series at:
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