Yesterday, we generated the formula for the sum of an arithmetic sequence.

Today, we will use the same approach to determine the formula for the sum of a geometric sequence.

Determine the sum of the Geometric Sequence

2 + 4 + 8 + 16 = 30Develop an algebraic methodS = 2 + 4 + 8 +

16 2S = 0 + 4 + 8 + 16 + 322S = 4 + 8 + 16 + 32

S = 2 + 4 + 8 + 16 + 0

-2 + 0 + 0 + 0 +32 = 30

Similar to an Arithmetic Sequence, these ideas can be extended to a

general formula

Sum of a Geometric Series

Sn = a(rn –1)

r - 1

S4 = 2(24 – 1) 2 – 1

= 2(15) 1 = 30

Determine the sum of the GS

2 + 4 + 8 + 16 =

30

a = 2, r = 2, n = 4

S10 = 24[(-0.5)10 – 1]

-0.5 – 1 = 24(-0.999) -1.5 = 15.984

Determine the sum of the first 10 terms of the GS

24 – 12 + 6 – 3 + …

a = 24, r = -0.5, n = 10

Remember:

If you are not given the number of terms (n), you can use the term formula to find it!!!

Pg 476[1-3]a,c,e7,10,12