Question

This is an example of an arithmetic series: 6 + 8 + 10 + 12 + . . . + (4 + 2n) + . . .

True or False?

Answer 1

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

`6,\ 8,\ 10,\ 12,\ \ldots,\ 4+2n`

is arithmetic, and thus the series

`6 + 8 + 10 + 12 + \ldots + (4+2n)`

is arithmetic as well.