1. Lake Zurich High School
Arithmetic
Sequences & Series
By: Jeffrey Bivin
Lake Zurich High School
Last Updated: April 28, 2006

2. Arithmetic Sequences 5, 8, 11, 14, 17, 20, … 3n+2, …

3. nth term of arithmetic sequence
an = a1 + d(n – 1)

4. Find the nth term of an arithmetic sequence
First term is 8
Common difference is 3
an = a1 + d(n – 1)
an = 8 + 3(n – 1)
an = 8 + 3n – 3
an = 3n + 5

5. an = a1 + d(n – 1) an = -6 + 7(n – 1) an = -6 + 7n – 7 an = 7n - 13
Finding the nth term
First term is -6
common difference is 7
an = a1 + d(n – 1)
an = (n – 1)
an = n – 7
an = 7n - 13

6. an = a1 + d(n – 1) an = 23 + -4(n – 1) an = 23 - 4n + 4 an = -4n + 27
Finding the nth term
First term is 23
common difference is -4
an = a1 + d(n – 1)
an = (n – 1)
an = n + 4
an = -4n + 27

7. an = a1 + d(n – 1) a100 = 5 + 6(100 – 1) a100 = 5 + 6(99)
Finding the 100th term
5, 11, 17, 23, 29, . . .
an = a1 + d(n – 1)
a100 = 5 + 6(100 – 1)
a100 = 5 + 6(99)
a100 =
a100 = 599
a1 = 5
d = 6
n = 100

8. an = a1 + d(n – 1) a956 = 156 + -16(956 – 1) a956 = 156 - 16(955)
Finding the 956th term
a1 = 156
d = -16
n = 956
156, 140, 124, 108,
an = a1 + d(n – 1)
a956 = (956 – 1)
a956 = (955)
a956 =
a956 =

9. Find the Sum of the integers from 1 to 100

10. Summing it up Sn = a1 + (a1 + d) + (a1 + 2d) + …+ an
Sn = an + (an - d) + (an - 2d) + …+ a1

11.
a1 = 1
an = 19
n = 7

12.
a1 = 4
an = 24
n = 11

13. Find the sum of the integers from 1 to 100
a1 = 1
an = 100
n = 100

14. Find the sum of the multiples of 3 between 9 and 1344
Sn =
Jeff Bivin -- LZHS
Jeff Bivin -- LZHS

15. Find the sum of the multiples of 7 between 25 and 989
Sn =
Jeff Bivin -- LZHS

16. Evaluate
a1 = 16
an = 82
d = 3
n = 23
Sn =

17. Evaluate Sn = -29 - 31 - 33 + . . . - 199 a1 = -29 an = -199 d = -2

18. Find the sum of the multiples of 11 that are 4 digits in length
an = 9999
d = 11
Sn =
Jeff Bivin -- LZHS

19. Review -- Arithmetic
Sum of n terms
nth term