Find the sum of the first 9 terms of the following sequence. Round to the nearest hundredth if necessary. 8,quad-4,quad2,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 9 terms of the following sequence. Round to the nearest hundredth if necessary.  8,quad-4,quad2,dots Sum of a finite geometric series:  S_(n)=(a_(1)-a_(1)r^(n))/(1-r) Answer:

Bytelearn · Accepted Answer

Identify sequence type: First, we need to identify the type of sequence we are dealing with. The sequence 8, -4, 2, ... appears to be a geometric sequence because each term is obtained by multiplying the previous term by a common ratio. To find the common ratio (r), we divide the second term by the first term. r = (-4) / 8 = -1/2Calculate common ratio: Next, we use the formula for the sum of the first n terms of a geometric series, which is: S_n = (a_1 - a_1 * r^n) / (1 - r) where S_n is the sum of the first n terms, a_1 is the first term, r is the common ratio, and n is the number of terms.Use sum formula: We plug in the values we know into the formula to find the sum of the first 9 terms: a_1 = 8 (the first term) r = -1/2 (the common ratio) n = 9 (the number of terms we want to sum) S_9 = (8 - 8 * (-1/2)^9) / (1 - (-1/2))Calculate (-1/2)^9: Now we calculate the value of (-1/2)^9: (-1/2)^9 = -1/512Substitute into formula: We substitute this value into the sum formula: S_9 = (8 - 8 * (-1/512)) / (1 - (-1/2)) S_9 = (8 - 8 * (-1/512)) / (1 + 1/2) S_9 = (8 - (-1/64)) / (3/2)Simplify expression: We simplify the expression: S_9 = (8 + 1/64) / (3/2) S_9 = (512/64 + 1/64) / (3/2) S_9 = (513/64) / (3/2)Divide by reciprocal: To divide by a fraction, we multiply by its reciprocal: S_9 = (513/64) * (2/3) S_9 = 513/96Simplify fraction: We simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 3: S_9 = 171/32Convert to decimal: Finally, we convert the fraction to a decimal to round to the nearest hundredth if necessary: S_9 ≈ 5.34375 Rounded to the nearest hundredth, S_9 ≈ 5.34

Find the sum of the first $9$ terms of the following sequence. Round to the nearest hundredth if necessary. $\newline$ $8, \quad-4, \quad 2, \ldots$ $\newline$ 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 trigonometric functions using a calculator

Related topics