How many terms are needed in the series 11+16+21+26 + to exceed 450

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The discussion revolves around determining how many terms are needed in the series 11+16+21+26 to exceed 450. The participant initially attempts to use the formula Sn=n/2(2u1+(n-1)d) but encounters confusion in their calculations. They mistakenly simplify the quadratic equation, leading to an incorrect result. After clarification, they correctly solve the quadratic equation 5n^2 + 17n - 910 = 0, ultimately arriving at the correct answer of 12 terms needed to exceed 450. The conversation highlights the importance of accurately solving quadratic equations in series problems.
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Homework Statement


How many terms are needed in the series 11+16+21+26...+ to exceed 450
d=5


Homework Equations


Sn=n/2(2u1+(n-1)d)


The Attempt at a Solution


(455 because is term exceeding 450 by the d of 5)
455=n/2(22+5n-5)
455=17n+5n2
455/17=5n2

Calculator work,
but the answer I get is not 12. The textbook says the answer is 12 :(
 
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Daaniyaal said:

Homework Statement


How many terms are needed in the series 11+16+21+26...+ to exceed 450
d=5


Homework Equations


Sn=n/2(2u1+(n-1)d)


The Attempt at a Solution


(455 because is term exceeding 450 by the d of 5)
455=n/2(22+5n-5)
455=17n+5n2
455/17=5n2

Calculator work,
but the answer I get is not 12. The textbook says the answer is 12 :(
How do you go from 455=17n+5n2, which is correct,

to 455/17=5n2, which is incorrect?

You need to solve the quadratic equation, 5n2 + 17n -455 = 0 .
 
Yeah, I get 910= n (17 +5n) which 5n^2 +17n - 910 = 0
 
I solved the quadratic and got the right answer, thanks!
 

Thread 'Family of lines that are at a distance of 5 from the origin'

I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...
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