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3. The sum of the terms of an
arithmetic sequence forms an
arithmetic series.
The sum of the first n terms of a
sequence, called a partial sum, is
denoted by 𝑆 𝑛.
4. The sum of n a terms of an arithmetic
sequence is given by:
𝑖𝑓 𝑎 𝑛 𝑖𝑠 𝑔𝑖𝑣𝑒𝑛, 𝑆 𝑛 =
𝑛
2
𝑎1 + 𝑎 𝑛
𝑖𝑓 𝑎 𝑛 𝑖𝑠 𝑛𝑜𝑡 𝑔𝑖𝑣𝑒𝑛, 𝑆 𝑛 =
𝑛
2
2𝑎 + 𝑛 − 1 𝑑
5. Find the sum of the first 12 terms of the arithmetic
sequence 50, 47, 44, 41, 38, …
Solution: 𝑎 = 50, 𝑑 = −3, 𝑛 = 12
𝑆 𝑛 =
𝑛
2
2𝑎 + 𝑛 − 1 𝑑
𝑆 𝑛 =
12
2
2 50 + 12 − 1 − 3
𝑆12= 6 100 − 33 𝑺 𝟏𝟐= 402
6. Find the sum of the first 18 terms of the arithmetic
sequence 3, 5, 7, 9, 11, …
Solution: 𝑎 = 3, 𝑑 = 2, 𝑛 = 18
𝑆 𝑛 =
𝑛
2
2𝑎 + 𝑛 − 1 𝑑
𝑆 𝑛 =
18
2
2 3 + 18 − 1 2
𝑆18= 9 6 + 34 𝑺 𝟏𝟖= 40
7. Find the sum of the first 30 natural numbers.
Solution: 𝑎1 = 1, 𝑎 𝑛 = 30, 𝑛 = 30
𝑆 𝑛 =
𝑛
2
𝑎1 + 𝑎 𝑛
𝑆 𝑛 =
30
2
1 + 30
𝑆30= 15 31 𝑺 𝟑𝟎= 465
8. Find the sum of the first 50 multiples of 5.
Solution: 𝑎1 = 5, 𝑎 𝑛 = 50, 𝑛 = 50
𝑆 𝑛 =
𝑛
2
𝑎1 + 𝑎 𝑛
𝑆 𝑛 =
50
2
5 + 50
𝑆50= 25 55 𝑺 𝟓𝟎= 1375
9. Find the sum of all multiples of 3 between 1 and 100.
Solution: 𝑎1 = 3, 𝑎 𝑛 = 99, 𝑑 = 3
First, we determine how many multiples
of 3 there are between 1 and 100.
𝑎 𝑛 = 𝑎 + 𝑛 − 1 𝑑
99 = 3 + 𝑛 − 1 3
99 = 3 + 3𝑛 − 3
99 = 3𝑛
𝒏 = 𝟑𝟑
𝑆 𝑛 =
𝑛
2
𝑎1 + 𝑎 𝑛
𝑆33 =
33
2
3 + 99
𝑺 𝟑𝟑 = 1, 683
10. Find the sum of all multiples of 6 between 1 and 100.
Solution: 𝑎1 = 6, 𝑎 𝑛 = 96, 𝑑 = 6
First, we determine how many multiples
of 6 there are between 1 and 100.
𝑎 𝑛 = 6 + 𝑛 − 1 𝑑
96 = 6 + 𝑛 − 1 6
96 = 6 + 6𝑛 − 6
96 = 6𝑛
𝒏 = 𝟏𝟔
𝑆 𝑛 =
𝑛
2
𝑎1 + 𝑎 𝑛
𝑆33 =
16
2
6 + 96
𝑺 𝟑𝟑 = 𝟖𝟏𝟔