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42 votes
42 votes
Find the sum of the first 7 terms of the

following sequence.

Round to the nearest
hundredth if necessary.

6,-10 ,50/3
Sum of a finite geometric series:

sn = a1-a1rn /1-r

Find the sum of the first 7 terms of the following sequence. Round to the nearest-example-1
User Marcos Curvello
by
3.4k points

2 Answers

17 votes
17 votes

Final answer:

To calculate the sum of the first 7 terms of the geometric sequence given, one must determine the common ratio, plug it into the sum formula for geometric series alongside the first term and the number of terms, and then calculate to obtain the sum rounded to the nearest hundredth.

Step-by-step explanation:

To find the sum of the first 7 terms of the given sequence 6, -10, 50/3, we first identify this as a geometric sequence by finding the common ratio (r). The common ratio is the factor that we multiply by to get from one term to the next. To find the ratio, we divide the second term by the first term:

r = -10 / 6 = -5 / 3

Now that we have the common ratio, we can use the formula for the sum of the first n terms of a geometric series:

sn = a1(1 - rn) / (1 - r)

For the sum of the first 7 terms, n = 7, a1 = 6, and r = -5/3:

s7 = 6(1 - (-5/3)7) / (1 - (-5/3))

Plugging in the values and simplifying, we get:

s7 = 6(1 - (-78125/2187)) / (1 + 5/3)

s7 = 6(2187 + 78125) / 2187) / (8/3)

s7 = 6(802312 / 2187) / (8/3)

s7 = (401156/1093.5) / (8/3)

Calculate this expression with a calculator to get the sum to the nearest hundredth.

User Sayse
by
2.6k points
21 votes
21 votes

Answer:

20078/243

Step-by-step explanation:

sn = a1-a1r^n/1-r

sn = a1 * 1-r^n/1-r

s7 = 6 * 1 - (-5/3)^7/1-(-5/3)

s7 = 6 * 10039/729

s7 = 6 * 10039/243*3

s7 = 2 * 10039/243

s7 = 20078/243

User Wantobegeek
by
2.8k points
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