Arithmetic Sequences & Partial Sums

Pre-CalculusLesson 9.2

An Arithmetic Sequence is a sequence whose consecutive terms have a common difference, d.

Find the common difference in each sequence.

1. 7, 11, 15, 19, ….4n + 3 2. 2, -3, -8, -13, … 7 – 5n

3. 1, , , …, … 4. 1, 4, 9, 16, … , n2, …

5. Find the first three terms of the arithmetic sequence with a1 = 300 and d = 50.

6. Find the first three terms of the arithmetic sequence with a1 = 220 and d = -25.

an = a1 + (n – 1)d

To find the nth term of an arithmetic sequence with first term a1 and

common difference d, use the following formula

7. Write a formula for the general term of the arithmetic sequence 2, 7, 12, 17…

8. Find the eighth term of the arithmetic sequence whose first term is 4 and whose common difference is – 7 .

9. Find the ninth term of the arithmetic sequence that begins with 2 and 9.

10. Find a6 when a1 = 13 and d = 4.

Sn =

Sum of a Finite Arithmetic Sequence, called Sn:

11.Find the sum: 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19

12. Find the sum of the integers from 1 to 100.

13. Find the 150th partial sum of the arithmetic sequence:

5, 16, 27, 38, 49…

14. Find the following sum:

25

1

95i

i