Unit 8

Synthetic division: x^2+7x+12 / x+4

-4] 1 +7 +12 | -4 -12 ———————- —> x+3 1 3 [0

Geometric series equation (infinite)

S=a1/1-r

Arithmetic series equation (finite)

Sn=(a1+an)n/2

Geometric series equation (finite)

Sn=a1 x (1-(r)^n)/(1-(r))

# of terms: 1+3+5+7+...+411

Term 1 + rate (n-1) = last term 1+2(n-1) =411 1+2n-2=411 2n-1=411 +1 +1 ——————- 2n=412 —> n=206

arithmetic sequence equation

a(n)=a0+nd

geometric sequence equation

a(n)=a1•r^n-1

Recursive sequence (geometric)

a0=?, a(n)=r x a(n-1)

Recursive sequence (arithmetic)

a1=?, a(n)=a(n-1) +/- rate

1,2,4,8,16 is an example of a(n)...

Geometric sequence

1+2+4+8+16 is an example of a(n)...

Geometric series

Arithmetic series equation (infinite)

No sum

Given one term and common difference (arithmetic): a11=-57 and d=-7

Number + (opposite sign of difference x term #) -57+7(11)

Given one term and common ratio (geometric): a6=-96 r=2

Number/r^n-1 -96/2^5

Given two terms (geometric): a2=-12 and a4=-3

#1 x r^term = #2 —> #1/answer -12 x r^2 = -3 —— —— —> r^2 = 1/4 —> r=1/2 —> -12/(1/2) -12 -12 =-24

Given two terms (arithmetic): a7=26 and a16=71

#2 - #1/term 2 - term 1 71-62 / 16-7 —-> 45/9=5

3,5,7,9 is an example of a(n)...

Arithmetic sequence

3+5+7+9 is an example of a(n)...

Arithmetic series

"D" is the...

Constant

In synthetic division, if x = a number...

Don't change the sign