Find the sum of the first 25 terms in this geometric series: 8+6+4.5". " Choose 1 answer: (A) 0.03 (B) 4.57 (C) 29.91 (D) 31.98

Identify Terms and Values: First, identify the first term (a1), common ratio (r), and number of terms (n) in the geometric series. The first term a1 is 8, the second term is 6, and the third term is 4.5. To find the common ratio r, we divide the second term by the first term: r = 6/8 = 0.75. The number of terms n is given as 25.Calculate Common Ratio: Use the formula for the sum of the first n terms of a geometric series: S_n = a1 * (1 - r^n) / (1 - r), where S_n is the sum of the first n terms. Plug in the values: S_25 = 8 * (1 - 0.75^25) / (1 - 0.75).Use Sum Formula: Calculate the sum using the values from the previous step. S_25 = 8 * (1 - 0.75^25) / (1 - 0.75) = 8 * (1 - 0.75^25) / 0.25 = 8 * (1 - 0.0000037252902984619140625) / 0.25 = 8 * (0.9999962747097015380859375) / 0.25 = 8 * 39999.8507880687713623046875 = 319999.4063045501708984375

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Find the sum of the first 25 terms in this geometric series:

8+6+4.5". "
Choose 1 answer:
(A) 0.03
(B) 4.57
(C)
29.91
(D) 31.98

Find the sum of the first $25$ terms in this geometric series: $\newline$ $8+6+4.5$ . $\newline$ Choose $1$ answer: $\newline$ (A) $0.03$ $\newline$ (B) $4.57$ $\newline$ (C) $29.91$ $\newline$ (D) $31.98$

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Math Problems

Algebra 2

Sum of finite series not start from 1

Full solution

Q. Find the sum of the first

25

terms in this geometric series:

\newline

8+6+4.5

\newline

Choose

1

answer:

\newline

(A)

0.03

\newline

(B)

4.57

\newline

(C)

29.91

\newline

(D)

31.98

Identify Terms and Values: First, identify the first term ( $a_1$ ), common ratio ( $r$ ), and number of terms ( $n$ ) in the geometric series. $\newline$ The first term $a_1$ is $8$ , the second term is $6$ , and the third term is $4.5$ . $\newline$ To find the common ratio $r$ , we divide the second term by the first term: $r = \frac{6}{8} = 0.75$ . $\newline$ The number of terms $n$ is given as $r$ $0$ .
Calculate Common Ratio: Use the formula for the sum of the first $n$ terms of a geometric series: $S_n = a_1 \times (1 - r^n) / (1 - r)$ , where $S_n$ is the sum of the first $n$ terms. $\newline$ Plug in the values: $S_{25} = 8 \times (1 - 0.75^{25}) / (1 - 0.75)$ .
Use Sum Formula: Calculate the sum using the values from the previous step. $\newline$ $S_{25} = 8 \times (1 - 0.75^{25}) / (1 - 0.75)$ $\newline$ $= 8 \times (1 - 0.75^{25}) / 0.25$ $\newline$ $= 8 \times (1 - 0.0000037252902984619140625) / 0.25$ $\newline$ $= 8 \times (0.9999962747097015380859375) / 0.25$ $\newline$ $= 8 \times 39999.8507880687713623046875$ $\newline$ $= 319999.4063045501708984375$