Geometric Sequences

Geometric Sequences- unlike arithmetic, geometric sequences are repeated multiplication.

ex.) 3, 6, 12, 24, 48, 96,...

3(2)=6, 6(2)=12, 12(2)=42, . . .

r = 2

(r) is the common ratio and r CANNOT equal zero

Geometric Partial Sum

~Take the first equation and multiply it by (r) to get the second equation

~ Subtract the two equations, cancel out like terms to end with:

~ Take out an Sn out from the left side and a1 from the right side so you end up with:

~divide both sides by (1-r) to get the final equation:

EX.) Let an be geometric sequence with a3 = 12 and a6 = 96. Find the 10th partial sum.

To find (r), first find the difference between n;

a6-a3= 3

3 becomes the power of r which equals the fraction of two terms.

take the cube root of 8

r= 2

Plug numbers into the partial sum formula

r= 2

a1= 3

n=10

Infinite Sum