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

## 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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SammyS
Staff Emeritus
Homework Helper
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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 :(
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
Mentor
Yeah, I get 910= n (17 +5n) which 5n^2 +17n - 910 = 0