allylearning101 allylearning101
  • 01-11-2018
  • Mathematics
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This is an example of an arithmetic series: 6 + 8 + 10 + 12 + . . . + (4 + 2n) + . . .

True or False?

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Аноним Аноним
  • 01-11-2018

True. A series is arithmetic if its terms come from an arithmetic sequence.

And a sequence is said to be arithmetic any of its two consecutive terms differ by a fixed difference, common to any consecutive pair.

As you can see, in this case, all terms differ by 2, so the sequence

[tex] 6,\ 8,\ 10,\ 12,\ \ldots,\ 4+2n [/tex]

is arithmetic, and thus the series

[tex] 6 + 8 + 10 + 12 + \ldots + (4+2n) [/tex]

is arithmetic as well.

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