9.2 Arithmetic Sequences

A Sequence is arithmetic if the differences between consecutive terms are

the same. So, the sequence

A sequence whose consecutive terms have a common difference is called an

Arithmetic sequence

                                                              

Explicit (18 years or Older) Term

Find the 100th term of the arithmetic sequence: 2, 5, 8, 11, …

Solution

=+ (n − 1)d

= 2 + (100 − 1)(3)

= 2 + (99)(3)

= 299

3 + 8 + 13 + 18 + …..

                  To find the common difference

         d = a_n+1 – a₁                   d = 13 – 8 = 5

                                             d = 18 – 13 = 5

                                             d = 5

3 + 8 + 13 + 18 + …..

                      Find the equation

                           a_n = a₁ + (n – 1)d

                           a_n = 3 + (n – 1)5

                           a_n = 3 + 5n – 5

                           a_n = -2 + 5n

Finding the Sum of Arithmetic Sequence

Find the sum of integers 8-49

=49/2(8+49)

=24.5(57)

=1396.5

Key Tips (stuff you Shouldn’t forget)

Recognize, write, and find

the nth terms of arithmetic

sequences.

• Find nth partial sums of

arithmetic sequences.

• Use arithmetic sequences to

model and solve real-life problems.

Historical Note A teacher of Carl Friedrich Gauss (1777–1855) asked him to add all the integers from 1to 100.When Gauss returned with the correct answer after only a few moments, the teacher could only look at him in astounded .

1+2+3+…+100 

100+99+98…+3+2+1  

101+101+101

100x101/2 = 5050

If  I was not to much Help I would really suggest you check out these videos.

https://www.youtube.com/watch?v=GIgiR367-Kk

https://www.youtube.com/watch?v=4El0_Vg7y38