sum_(k=0)^(29)-3(0.9)^(k)~~ Choose 1 answer: (A) -4.63*10^(13) (B) -28.7 (c) -1.65 (D) -0.14

Identify series type: Identify the type of series. The series given is a geometric series because each term is obtained by multiplying the previous term by a common ratio, which is 0.9 in this case.Use formula for sum: Use the formula for the sum of a finite geometric series. The sum S of a geometric series with first term a, common ratio r (where |r| < 1), and n terms is given by the formula: S = a(1 - r^n) / (1 - r) Here, a = -3 (the first term), r = 0.9 (the common ratio), and n = 30 (since we are summing from k=0 to k=29).Plug values and calculate: Plug the values into the formula and calculate the sum. S = -3(1 - 0.9^30) / (1 - 0.9) Now we need to calculate 0.9^30 and then the rest of the expression.Calculate 0.9^30: Calculate 0.9^30. 0.9^30 is a very small number, and for practical purposes, we can consider it to be close to 0 when subtracted from 1, given the context of the other answer choices. However, for accuracy, we should still calculate it.Calculate sum using approximation: Calculate the sum using the approximation that 0.9^30 is close to 0. S ≈ -3(1 - 0) / (1 - 0.9) S ≈ -3 / 0.1 S ≈ -30Check answer choices: Check the answer choices for the closest value to our calculation. The closest value to -30 is (B) -28.7. Therefore, the sum of the series is approximately -28.7.

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sum_(k=0)^(29)-3(0.9)^(k)~~
Choose 1 answer:
(A)
-4.63*10^(13)
(B) -28.7
(c) -1.65
(D) -0.14

$\sum_{k=0}^{29}-3(0.9)^{k} \approx$ $\newline$ Choose $1$ answer: $\newline$ (A) $-4.63 \cdot 10^{13}$ $\newline$ (B) $-28$ . $7$ $\newline$ (C) $-1$ . $65$ $\newline$ (D) $-0$ . $14$

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Algebra 1

Compare linear and exponential growth

Full solution

\sum_{k=0}^{29}-3(0.9)^{k} \approx

\newline

Choose

1

answer:

\newline

(A)

-4.63 \cdot 10^{13}

\newline

(B)

-28

7

\newline

(C)

-1

65

\newline

(D)

-0

14

Identify series type: Identify the type of series. The series given is a geometric series because each term is obtained by multiplying the previous term by a common ratio, which is $0.9$ in this case.
Use formula for sum: Use the formula for the sum of a finite geometric series. $\newline$ The sum $S$ of a geometric series with first term $a$ , common ratio $r$ (where |r| < 1), and $n$ terms is given by the formula: $\newline$ $S = \frac{a(1 - r^n)}{1 - r}$ $\newline$ Here, $a = -3$ (the first term), $r = 0.9$ (the common ratio), and $n = 30$ (since we are summing from $k=0$ to $k=29$ ).
Plug values and calculate: Plug the values into the formula and calculate the sum. $\newline$ $S = -3(1 - 0.9^{30}) / (1 - 0.9)$ $\newline$ Now we need to calculate $0.9^{30}$ and then the rest of the expression.
Calculate $0.9^{30}$ : Calculate $0.9^{30}$ . $0.9^{30}$ is a very small number, and for practical purposes, we can consider it to be close to $0$ when subtracted from $1$ , given the context of the other answer choices. However, for accuracy, we should still calculate it.
Calculate sum using approximation: Calculate the sum using the approximation that $0.9^{30}$ is close to $0$ . $\newline$ $S \approx -3(1 - 0) / (1 - 0.9)$ $\newline$ $S \approx -3 / 0.1$ $\newline$ $S \approx -30$
Check answer choices: Check the answer choices for the closest value to our calculation. $\newline$ The closest value to $-30$ is (B) $-28.7$ . Therefore, the sum of the series is approximately $-28.7$ .