Find the sum of the first 7 terms of the following sequence. Round to the nearest hundredth if necessary. 5,quad6,quad(36)/(5),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.  5,quad6,quad(36)/(5),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 given sequence is 5, 6, (36)/(5), ..., which suggests that it is a geometric sequence because each term after the first is obtained by multiplying the previous term by a common ratio (r).Find Common Ratio: To find the common ratio (r), we divide the second term by the first term. r = 6 / 5 = 1.2Calculate Sum Formula: Now that we have the common ratio, we can use the formula for the sum of the first n terms of a geometric series: 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, and r is the common ratio.Substitute Values: We are looking for the sum of the first 7 terms, so n = 7, a_1 = 5, and r = 1.2. Plugging these values into the formula, we get: S_7 = (5 - 5 * (1.2)^7) / (1 - 1.2)Calculate Exponent: Now we calculate (1.2)^7 and then substitute it back into the formula. (1.2)^7 ≈ 3.5832 S_7 = (5 - 5 * 3.5832) / (1 - 1.2)Simplify Expression: Substitute the value of (1.2)^7 into the formula and simplify. S_7 = (5 - 5 * 3.5832) / (1 - 1.2) S_7 = (5 - 17.916) / (-0.2)Perform Final Calculation: Now we perform the subtraction in the numerator and the division. S_7 = (-12.916) / (-0.2) S_7 ≈ 64.58

Find the sum of the first $7$ terms of the following sequence. Round to the nearest hundredth if necessary. $\newline$ $5, \quad 6, \quad \frac{36}{5}, \ldots$ $\newline$ 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