Find the sum of the first 7 terms of the following sequence. Round to the nearest hundredth if necessary. 27,quad-54,quad108,dots Sum of a finite geometric series: S_(n)=(a_(1)-a_(1)r^(n))/(1-r) Answer:

Question

Find the sum of the first 7 terms of the following sequence. Round to the nearest hundredth if necessary.  27,quad-54,quad108,dots Sum of a finite geometric series:  S_(n)=(a_(1)-a_(1)r^(n))/(1-r) Answer:

Bytelearn · Accepted Answer

Identify first term: Identify the first term (a_1) of the geometric sequence. The first term a_1 is 27.Determine common ratio: Determine the common ratio (r) of the sequence. To find the common ratio, divide the second term by the first term: r = -54 / 27 = -2.Use sum formula: Use the formula for the sum of the first n terms of a geometric series: S_n = (a_1(1 - r^n)) / (1 - r), where n is the number of terms. We need to find the sum of the first 7 terms, so n = 7.Substitute values: Substitute the values of a_1, r, and n into the formula. S_7 = (27(1 - (-2)^7)) / (1 - (-2))Calculate (-2)^7: Calculate the value of (-2)^7. (-2)^7 = -128.Simplify expression: Substitute the value of (-2)^7 into the formula. S_7 = (27(1 - (-128))) / (1 - (-2))Substitute simplified expression: Simplify the expression inside the parentheses. 1 - (-128) = 1 + 128 = 129.Simplify denominator: Substitute the simplified expression into the formula. S_7 = (27 * 129) / (1 + 2)Calculate sum: Simplify the denominator. 1 + 2 = 3.Calculate the sum S_7. S_7 = (27 * 129) / 3 S_7 = 3483 / 3 S_7 = 1161

Find the sum of the first $7$ terms of the following sequence. Round to the nearest hundredth if necessary. $\newline$ $27, \quad-54, \quad 108, \ldots$ $\newline$ Sum of a finite geometric series: $\newline$ $S_{n}=\frac{a_{1}-a_{1} r^{n}}{1-r}$ $\newline$ Answer:

Full solution

More problems from Find the roots of factored polynomials

Related topics