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