Week 2 – Precalc 11

This week in precalc 11 we learned about geometric series.

Geometric series is the sum of the terms of a geometric sequences, a series with a constant ratio between successive terms. For example, a geometric series would be 6 + 12 + 24 + 48 + . . . The common ratio is the ratio between two numbers in a geometric sequence. To determine the common ratio, you can just divide each number from the number preceding it in the sequence (formula: r = a(n) / a(n – 1) ).

We also learned how the formula for determining the sum of the first n terms in any geometric series using the formula: 

Here’s an example on how to apply this

Find S_{10} for the geometric series 80 + 60 + 45. . .

a = 80

r = 0.75

S_{10} = 80 ( ( 0.75^{10} ) – 1) ÷ ( o.75 – 1)

S_{10} = 301.98

Another example       ↓

For the geometric series 3, 9, 27. . . 6561, determine how many terms it has and then calculate its sum.

r = 3

a = 3

t_n = 6561

 

t_n = a ( r^{n-1}

6561 = 3 ( 3^{n-1}

2187 = ( 3^{n-1}

3^73^{n-1}

7 = n – 1

8 = n

 

S_{8} = 3 ( 3^8  – 1 ) ÷  ( 3 – 1)

S_{8} = 9840

 

 

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