arithmetic/geometric sequences, HELP NEEDED BADLY Options

[Gigi]

Yeah. Both my friend and I are totally stuck on this.

3+7+11+15...
How many terms have a sum of less than 500?

Formula for general term (where n=# of terms, a=first term, d=common difference):
Term of n = a+(n-1)d

Okay. So you need to find the general term first, right?
Term of n = 3+(n-1)4
Term of n = 4n-1

Formula for sum of arithmetic sequence (where n=# of terms, a=first term, d=common difference):
Sum of n = n/2(a+term of n)

So that would be...
Sum of n = n/2(3+4n-1)
Sum of n = n/2(4n+2)
Sum of n = 2(n^2)+n

To find the terms with sum less than 500, you'd go:
2(n^2)+n < 500

...right? The thing is. How do you solve that?

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Second question. How do you solve for "n" in:

3^(n-1)=729?

[FREEcandies]

She has all the equations (or inequations) right, she just needs to do some algebra to solve for them.

For the inequality (2n^2)+n < 500. You just treat the < sign like a = and solve using the quadratic formula.

For the second problem 3^(n-1)=729, you use the laws of exponents to solve.

n = [729^(1/3)] + 1