Arithmetic and Geometric Series and Sequences

Arithmetic Sequences

sn = n(t1 + tn)/2

To find the sum of a finite arithmetic series, you need to know three things. The first term, the last term and the number of terms.

1) Find the sum of the first 30 terms of 5 + 9 + 13 + 17 + . . .

t1 = 5, and that's pretty obvious!

We need the 30th term. Use the defintion of an arithmetic sequence.

t30 = 5 + 29.4 = 121

Therefore: S30 = 30(5 + 121)/2 = 1890

Answer: n = 30

Geometric Sequence

Sn = t1 (r^n-1)

2) Find the sum of the first 10 terms of the geometric series: 4, 8, 16, 32, 64, . . .

r = 2

t10 = 4 . 29 = 2048

Therefore: S10 = 4(1-210)/(1 - 2) = 4 . 1023 = 4092

Answer: t1 = 4

Geometric series and sequences video:

http://www.youtube.com/watch?v=4coX-DWv5Hw&feature=relmfu

Arithmetic series and sequences video:

http://www.youtube.com/watch?v=k_bGU3_coYE&feature=relmfu