yesterday, we generated the formula for the sum of an arithmetic sequence. today, we will use the...
Post on 03-Jan-2016
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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
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