Given the sequence, 26, 13, 6.5, ..... find a) the 10th term and b) the sum of the first 18 terms
1 answer:
Answer:
a) 10th term is 0.051
b) The sum of first 18 terms of given sequence is 51.48
Step-by-step explanation:
We are given the sequence 26, 13, 6.5, ..... we need to find
a) 10th term
b) Sum of first 18 terms
Before solving we need to determine if the sequence is arithmetic or geometric
The sequence is arithmetic if common difference d is same.
The sequence is geometric if common ratio r is same.
Finding common difference d: 13-26 = -13, 6.5-13= -6.5
As common difference is not same so, the sequence is not arithmetic.
Finding common ratio r : 13/26 =0.5, 6.5/13= 0.5
As common ratio is same so, the sequence is geometric.
a) Finding common difference: 13-26 = -13, 6.5-13= -6.5
As common difference is not same so, the sequence is not arithmetic.
a) 10th term
The formula to find 10th term is:
We have a₁=26 and r = 0.5 n=10
So, 10th term is 0.051
b) Sum of first 18 terms
The formula to find sum of geometric series is:
where a= 1st term, r = common ratio and n= number of terms
In the given sequence we have
a=26, r=0.5 and n=18
Finding sum of first 18 terms
So, sum of first 18 terms of given sequence is 51.48
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1) The angle of elevation is the angle between the horizontal and the light of sight from the object to the observer (see picture 1).
2) A lot of the units are from work done by an Indian astronomer. The line of sight (light blue in picture 1) is r = 3438 (I think you might have forgotten to finish writing the number). r, or 3438, is the distance from the earth to the sun used by Indian Astronomers.
3) The table shows units in jya(θ<span>°). Jya is a Sanskrit (ancient Indian language) word. It stands for the length of half of a chord that connects two endpoints of a circle (kinda confusing and more information than you need to know - but it's the green line in picture 2).
What's important is: </span>jya(θ°) = r*sin(θ°)
Now let's tackle the problem:
1) You know that the angle of elevation is 67.5°. Using the chart, the only important value is the second from the bottom. jya(67.5°) = 3177.
2) Remember that jya(θ°) = r*sin(θ°).
Also remember that sine of an angle is
. In this problem, r, the distance from the earth to the sun, happens to be the hypotenuse of the triangle since its the longest edge.
3) Notice that you're dividing jya(θ°) (aka r*sin(θ°)) by r = 3438. That will give you sin(θ°) by itself. Then you're multiplying that sin(θ°) by 1 AU, which we are told is the actual distance of the hypotenuse/distance from earth to sun. Since sine = that gives you the apparent length of the opposite side = apparent height of the sun.
The math is a bit weird, but you're basically multiplying sine by the apparent distance 1AU to get the apparent height, instead of multiplying sine by the estimated height r = 3438. Dividing 3177 by 3438 gives you sin(67.5°). Then multiplying sin(67.5°) by the apparent hypotenuse, 1AU, gives you the apparent height. That's how I'm understanding it!
1) The angle of elevation is the angle between the horizontal and the light of sight from the object to the observer (see picture 1).
2) A lot of the units are from work done by an Indian astronomer. The line of sight (light blue in picture 1) is r = 3438 (I think you might have forgotten to finish writing the number). r, or 3438, is the distance from the earth to the sun used by Indian Astronomers.
3) The table shows units in jya(θ<span>°). Jya is a Sanskrit (ancient Indian language) word. It stands for the length of half of a chord that connects two endpoints of a circle (kinda confusing and more information than you need to know - but it's the green line in picture 2).
What's important is: </span>jya(θ°) = r*sin(θ°)
Now let's tackle the problem:
1) You know that the angle of elevation is 67.5°. Using the chart, the only important value is the second from the bottom. jya(67.5°) = 3177.
2) Remember that jya(θ°) = r*sin(θ°).
Also remember that sine of an angle is
3) Notice that you're dividing jya(θ°) (aka r*sin(θ°)) by r = 3438. That will give you sin(θ°) by itself. Then you're multiplying that sin(θ°) by 1 AU, which we are told is the actual distance of the hypotenuse/distance from earth to sun. Since sine =
The math is a bit weird, but you're basically multiplying sine by the apparent distance 1AU to get the apparent height, instead of multiplying sine by the estimated height r = 3438. Dividing 3177 by 3438 gives you sin(67.5°). Then multiplying sin(67.5°) by the apparent hypotenuse, 1AU, gives you the apparent height. That's how I'm understanding it!
Answer:
, or
Step-by-step explanation:
To divide, we can use fractions. So we can say that 0.04 divided by n is , or
.