Geometric Sequences:
"multiplies" ratio= r
Formula:
tn= ar^ n-1
r= multiplier
tn = value n= nth position
*note: if you want to find the multiplier r= t2/a ( the 2nd number divided by the first)
Example 1:
In the following sequence: 2, 6, 18 54 ..... Find
a) t6 b) t10
r= 6/2=3 = 2(3) ^ 9
54x3= 162 t5 = 39366
162x 3= 484 t6
c) which term is 9 565 938
9565938 = 2(3)^ n-1 step1: divided by first number
2 2 step 2: log both sides
log 4782969 = (n-1) log3 step 3: isolate (n-1)
log 3 log3
14 = n-1 step 4: solve
15 = n
9565938 = t5
Series:
A series is the sum of a sequence
S= add t= find number
Formulas:
Sn = a(1 - r^n) or Sn = a- rl
1 - r 1 - r
Sn: series ( sum) r: ratio l: last term> tn
a: first # n: how many terms there is
Example:
Find the sum of the series
5 + 15+ 45 +.......... + 885 735
Sn = a - rl Sn= 5 - 3(885 735)
1 - r 1 -3
= 1, 328, 600
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