Find the sum of the first 8 terms of the following sequence. Round to the nearest hundredth if necessary. 64,quad80,quad100,dots Sum of a finite geometric series: S_(n)=(a_(1)-a_(1)r^(n))/(1-r) Answer:

Identify sequence type: First, identify the type of sequence given. The sequence 64, 80, 100, ... suggests that it is an arithmetic sequence because the difference between consecutive terms is constant.Determine common difference: Determine the common difference (d) of the arithmetic sequence by subtracting the first term from the second term: d = 80 - 64 = 16.Use sum formula: Use the formula for the sum of the first n terms of an arithmetic sequence: S_n = n/2 * (2a_1 + (n - 1)d), where S_n is the sum of the first n terms, a_1 is the first term, and d is the common difference.Plug values into formula: Plug the values into the formula to find the sum of the first 8 terms: S_8 = 8/2 * (2*64 + (8 - 1)*16).Simplify expression: Simplify the expression: S_8 = 4 * (128 + 7*16) = 4 * (128 + 112) = 4 * 240.Calculate sum: Calculate the sum: S_8 = 4 * 240 = 960.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Find the sum of the first 8 terms of the following sequence. Round to the nearest hundredth if necessary.

64,quad80,quad100,dots
Sum of a finite geometric series:

S_(n)=(a_(1)-a_(1)r^(n))/(1-r)
Answer:

Find the sum of the first $8$ terms of the following sequence. Round to the nearest hundredth if necessary. $\newline$ $64, \quad 80, \quad 100, \ldots$ $\newline$ Sum of a finite geometric series: $\newline$ $S_{n}=\frac{a_{1}-a_{1} r^{n}}{1-r}$ $\newline$ Answer:

View step-by-step help

Home

Math Problems

Algebra 2

Sum of finite series not start from 1

Full solution

Q. Find the sum of the first

8

terms of the following sequence. Round to the nearest hundredth if necessary.

\newline

64, \quad 80, \quad 100, \ldots

\newline

Sum of a finite geometric series:

\newline

S_{n}=\frac{a_{1}-a_{1} r^{n}}{1-r}

\newline

Answer:

Identify sequence type: First, identify the type of sequence given. The sequence $64, 80, 100, \ldots$ suggests that it is an arithmetic sequence because the difference between consecutive terms is constant.
Determine common difference: Determine the common difference $d$ of the arithmetic sequence by subtracting the first term from the second term: $d = 80 - 64 = 16$ .
Use sum formula: Use the formula for the sum of the first $n$ terms of an arithmetic sequence: $S_n = \frac{n}{2} \times (2a_1 + (n - 1)d)$ , where $S_n$ is the sum of the first $n$ terms, $a_1$ is the first term, and $d$ is the common difference.
Plug values into formula: Plug the values into the formula to find the sum of the first $8$ terms: $S_8 = \frac{8}{2} \times (2\times64 + (8 - 1)\times16)$ .
Simplify expression: Simplify the expression: $S_8 = 4 \times (128 + 7\times16) = 4 \times (128 + 112) = 4 \times 240$ .
Calculate sum: Calculate the sum: $S_8 = 4 \times 240 = 960$ .