Core Connections Integrated III, 2015
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Core Connections Integrated III, 2015 View details
2. Section 10.2
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Exercise 97 Page 525

Practice makes perfect
a

Examining the geometric sequence, we notice that it has an initial value of 3 and a common ratio of 10. Therefore, to go from one term to the next we have to multiply by 10. This makes it quite easy to calculate terms since, when multiplying by 10, we just add a 0 to the end of the previous term.

3, 30, 300, 3000, 30 000, 300 000 Below, we have calculated the sum of this series. 3+ 30+ 300+ 3000+ 30 000+ 300 000 ⇓ 3 3 3 3 3 3
b

To calculate the sum of a geometric series, we use the following formula.

S_n=a_1(1-r^n)/1-r By substituting the first term, the number of terms, and the common factor, we can calculate the sum of the series.

S_n=a_1(1-r^n)/1-r
S_6=3(1-10^6)/1-10
â–¼
Evaluate right-hand side
S_6=3(1-10^6)/-9
S_6=3(1-1 000 000)/-9
S_6=3(- 999 999)/-9
S_6=3(999 999)/9
S_6=3(111 111)
S_6=333 333

c

The first n terms of the series can be written in summation notation in the following way.

∑_(k=1)^n (3* 10^(k-1))