The series: 2 + 4 + 6 +.... is an arithmetic series
The sum of T41 to T47 is 616
How to determine the sum of the series
The series is given as:
2 + 4 + 6 +....
The above series is an arithmetic series with the following parameters:
Initial value, a = 2
Common difference, d = 2
Start by calculating S40 using the sum of n terms formula
[tex]S_n = \frac n2 * [2a + (n - 1)d][/tex]
So, we have:
[tex]S_{40} = \frac {40}2 * [2*2 + (40 - 1)*2][/tex]
[tex]S_{40} = 1640[/tex]
Calculate S47 using the same formula
[tex]S_{47} = \frac {47}2 * [2*2 + (47 - 1)*2][/tex]
[tex]S_{47} = 2256[/tex]
Subtract S40 from S47
[tex]S_{47} - S_{40} = 2256 - 1640[/tex]
[tex]S_{47} - S_{40} = 616[/tex]
Hence, the sum of T41 to T47 is 616
Read more about arithmetic series at:
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