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Answer:
127.5
Step-by-step explanation:
The given series is 26 + 24.5 + 23 + 21.5 + ... - 17.5
The first term of this series is a=26
The common difference is d=24.5-26=-1.5
The last term of the series is -17.5
The nth term is given by:
n=30
The sum of the series:
Consider the attached ellipse. Let the sun be at the right focus. Then perihelion is at right vertex on the x-axis and aphelion is at the left vertex on the x-axis.
The distances:
- from perihelion to the sun in terms of ellipse is a-c;
- from aphelion to the sun in terms of ellipse is a+c.
Then
Add these two equations:
and subtract first equation from the second:
Note that thus
The equation for the planet's orbit is