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# Arithmetic Series $S_n=\frac{n}{2}[2a+(n-1)d]$ or $S_n=\frac{n}{2}(a+t_n)$

1. 1
Find the sum of the first 40 terms given the arithmetic series:
$$2+5+8+11+...$$
2. 2
Find the sum of the first 25 terms given the arithmetic series:
$$-3 -7 -11 -15-...$$
3. 3
Find $S_{30}$ given the arithmetic series:
$$24+19+14+9+...$$
4. 4
Find the sum given the arithmetic series:
$$3+5+7+9+...+71$$
5. 5
Find the sum given the arithmetic series:
$$25+18+11+4+...-59$$
6. 6
Find the sum given the arithmetic series:
$$4+7+10+13+...+127$$
7. 7
A theatre has 18 seats in the front row and 3 additional seats in each following row.

How many seats are there if the theatre has 20 rows?
8. 8
A log pile has 26 logs on the bottom row. each row above has one less log to form a triangular pile with 1 log at the top.

How many logs are there in the pile?
9. 9
Find the first four terms of the arithmetic series with:
$$t_{12}=35\; \quad S_{20}=610$$
Good test question!
10. 10
Find the first four terms of the arithmetic series with:
$$t_{5}=14\; \quad S_{10}=165$$
11. 11
The sum of the first four terms of an arithmetic sequence is $50$ and $S_{6}=93$. find the first three terms. Good test question!

$$e=mc^2$$