Find the sum of the first 9 terms in the following geometric series. Do not round your answer. 7+21+63+dots

Question

Find the sum of the first 9 terms in the following geometric series. Do not round your answer.  7+21+63+dots

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Identify first term and ratio: Identify the first term and the common ratio of the geometric series. The first term (a1) is 7. To find the common ratio (r), we divide the second term by the first term. r = 21 / 7 = 3Use formula for sum: Use the formula for the sum of the first n terms of a geometric series. The formula for the sum of the first n terms (Sn) of a geometric series is: Sn = a1 * (1 - r^n) / (1 - r), where a1 is the first term, r is the common ratio, and n is the number of terms.Plug values for first 9 terms: Plug the values into the formula to find the sum of the first 9 terms. We have a1 = 7, r = 3, and n = 9. S9 = 7 * (1 - 3^9) / (1 - 3)Calculate power of 3: Calculate the power of 3 to the 9th power. 3^9 = 19683Substitute value into formula: Substitute the value of 3^9 into the formula. S9 = 7 * (1 - 19683) / (1 - 3)Simplify expression and denominator: Simplify the expression inside the parentheses and the denominator. S9 = 7 * (1 - 19683) / (-2) S9 = 7 * (-19682) / (-2)Perform multiplication and division: Perform the multiplication and division to find the sum. S9 = 7 * 9841 S9 = 68887

Find the sum of the first $9$ terms in the following geometric series. Do not round your answer. $\newline$ $7+21+63+\ldots$

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Find the sum of the first $9$ terms in the following geometric series. Do not round your answer. $\newline$ $7+21+63+\ldots$