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WEEK 2
CLASS: SS1
TOPIC: SERIES
CONTENT:
Sub – Topic: DEFINITION OF SERIES/ARITHMETIC SERIES
Series is the summation (addition) of the terms of a sequence. For example, the series equivalent of the sequence 1,2,3, 4, is 1+2+3+4+…. If the sequence contains finite numbers of terms, then the corresponding series is finite. If the sequence contains infinite numbers of terms, then the corresponding series is infinite.
These are series formed from an arithmetic progression. e.g.
1 + 4 + 7 + 10 + …
In general, if Sn is the sum of n terms of an arithmetic series then
Sn = a + (a + d) + (a + 2d) + … + (l – d) +l …………………….. (1)
Where l is the nth term, a is the first term and d is the common difference.
Rewriting the series above starting with the nth/last term, we have.
Sn = l +(l – d) + (l – 2d) +… + (a + d) + a ………………………….(2)
Adding equation (1) and (2) we have
2Sn = (a + l) + (a + l) + … + (a + l) + (a + l) in n places
2Sn = n(a + l)
\Sn = n/2(a + l)
But l is the nth term i.e a + (n – 1) d
Sn= n/2{a +a + (n – 1)d}
\Sn = n/2 {2a + (n – 1)d}
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