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

[Daaniyaal]

Homework Statement

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

Homework Equations

S_n=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 :(

 

[SammyS]

Homework Statement

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

Homework Equations

S_n=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 .

 

[jedishrfu]

Yeah, I get 910= n (17 +5n) which 5n^2 +17n - 910 = 0

 

[Daaniyaal]

I solved the quadratic and got the right answer, thanks!