Following is the para from Higher Algebra by Hall and Knight
Quantities are said to be in Arithmetical Progression when they increase or decrease by a common difference. Thus each of the following
seriesforms an Arithmetical Progression3, 7, 11, 15,...
8, 2, -4, -10,...
a, a + d, a + 2d, a + 3d,...
I suspect the word 'series' is wrongly used. It should be 'sequence'. As far as I know 'series' is "A series is the sum of terms of sequence."
So, my concern is to reconfirm that I am correct or not.
Thanks in advance!
You are right, but I suspect that book was published more than a century ago. About then, mathematical terms were vague, not as defined as we have them today. So they would have used the terms sequence and series loosely and interchangeably, sometimes.
When reading ancient material (where you cannot find an updated edition) always beware that there may be differences in the way words similar in form are used.