Given the geometric series:16+2+1/4... find the sum of the geometric progression up to the 6th term
Answers
The sum of the geometric progression up to the 6th term is 512/7
To find the sum of a geometric series, you can use the formula for the sum of a finite geometric series:
Where:
- Sₙ is the sum of the first n terms of the series.
- a is the first term of the series.
- r is the common ratio.
- n is the number of terms in the series.
In your case, you have the geometric series: 16, 2, 1/4, ...
1. Identify the values for the formula:
- The first term (a) is 16.
- The common ratio (r) is found by dividing the second term by the first term: 2/16 = 1/8.
- You want to find the sum of the first 6 terms (n = 6).
2. Plug these values into the formula and calculate S₆:
S₆ = (16(1 - (1/8)⁶))/(1 - 1/8)
Now, calculate the individual terms in the formula:
S₆ = (16(1 - 1/262144))/(7/8)
S₆ = (16(262143/262144))/(7/8)
S₆ = ((4194288/262144)/(7/8)
Now, perform the division:
S₆ = (4194288/262144) \* (8)/(7)
S₆ = 64 * 8/7
Now, multiply:
S₆ = 512/7
So, the sum of the geometric progression up to the 6th term is 512/7
Learn more about geometric series here
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Answers
30.80 + 1.20 = 32.00
Falling by 6.25% means it ends up being 93.75% of what it used to be (100% - 6.25% = 93.75%)
Wednesday:
32.00 * 0.9375 = 30
Thursday:
30 * 0.96 = 28.8
Friday:
28.8 * 1.025 = 29.52
Net change means you subtract to get the difference.
Net change = Final - initial
= 29.52 - 30.80
= -1.28
The stock fell $1.28
Hope this helps!
I need help with that ASAP please
Answers
Answer:
a<5
Step-by-step explanation:
a/5<1
5*a/5<1*5
a<5
C. P = 5x + 4y
D. P = 4x + 5y
Answers
Answer:
Option C is correct that is P=5x+4y
Step-by-step explanation:
We have given She has 15 eggs and 16 cups of flour in her pantry. Her pumpkin bread recipe uses 2 eggs and 3 cups of flour. Her coffee cake recipe uses 3 eggs and 4 cups of flour
Let x represents number of loaves of pumpkin bread
And y represents the number of loaves of coffee cake Susan bakes
Since, She plans to sell pumpkin bread loaves for $5 each and coffee cake loaves for $4 each.
Hence, P=5x+4y
Therefore, option C is correct.
Answers
Answers
Answer:
Hi,
Step-by-step explanation:
Answer:
Step-by-step explanation:
5%
20%
25%
Answers
The probability that the first card will be red, and the second card will be blue is 5%
What is probability?
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.
P(event) = favorable outcomes / possible outcomes
p(red) = 1 / 5
p(blue) = 1 / 4 (since, the card is not replaced)
We know that, the probability that the first card will be red, and the second card will be blue: p(red then blue) = p(red) × p(blue)
p(red then blue) = 1 / 5 × 1 / 4 = 1 / 20
= 5%
Hence, the probability that the first card will be red, and the second card will be blue is 5%
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Hi there!
First, for any of the five cards being drawn, there is a 1/5 chance, or 20%. So, the probability of a red card being drawn is 1/5. Then, since the card is not replaced, it becomes a 1/4, or 25%, chance of any card being drawn (besides red). So, the probability of a blue card being drawn is 1/4. So in order to find what the question is asking, we'll need to multiply the two fractions together.
1/5 x 1/4 = 1/20
1/20 = 5%
Therefore, the correct answer is 5%, or the second option.
Hope this helps!! :)