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

Question

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

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Identify terms and ratio: 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.Use sum formula: 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, a1 is the first term, r is the common ratio, and n is the number of terms.Plug in values: Plug the values into the formula: S_25 = 8 * (1 - 0.75^25) / (1 - 0.75).Calculate sum: Calculate the sum: S_25 = 8 * (1 - 0.75^25) / (1 - 0.75). First, calculate 0.75^25, then subtract it from 1, and finally divide by (1 - 0.75) and multiply by 8.Perform calculations: Perform the calculations: 0.75^25 is a very small number, so for practical purposes, it can be considered as approximately 0 when subtracted from 1. Therefore, S_25 ≈ 8 * (1 - 0) / (1 - 0.75) = 8 / 0.25.Complete division: Complete the division: 8 / 0.25 = 32.Final sum: The sum of the first 25 terms in the geometric series is approximately 32, which corresponds to answer choice (D) 31.98, considering that the actual calculation might have a slight difference due to rounding in the intermediate steps.

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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Find the sum of the first 252525 terms in this geometric series:\newline8+6+4.5+...8+6+4.5+...8+6+4.5+... \newlineChoose 111 answer:\newline(A) 0.030.030.03\newline(B) 4.574.574.57\newline(C) 29.9129.9129.91\newline(D) 31.9831.9831.98

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) $31.98$