SOLUTION: How many terms in the series 5+9+13=......+tn are less than 500? How many terms are neede for a sum of less than 500?

Question 1011672: How many terms in the series 5+9+13=......+tn are less than 500? How many terms are neede for a sum of less than 500?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
The series is 4n+1
4n+1=497 when 4n=496 and n=124.
There are 124 terms.
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sum=(n/2)(a1+an)
a1=5
a2=9
a3=13
a4=17
sum<500
500>(n/2)(5+4n+1)=(n/2)(4n+6)
1000>4n^2+6n
4n^2+6n-1000<0
2n^2+3n-500<0
n=(1/4)(-3+/- sqrt (9+4000); sqrt 4009=63.31
n=(1/4)(60.31)
n=15.07
so n=15 will be correct
n=15, term is 61
sum=(15/2)(5+61)=66*7.5=493
15 terms

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