Function problem

[Imum Coeli]

Hi.

I have a problem and I'm not quite even sure what it means so I'll copy it verbatim.

Question:
Let f(x) = 3x-1, and let x_i = 2+2(i/n). Evaluate the sum of f(x_i) for i=1,...,n as a formula in terms of n.

Notes:
All I can notice is assuming n is very large then f(x_i) is approximately 5 when i=1 and equal to 11 when i=n.
In all honesty I'm not even sure what exactly I'm looking for let alone how I go about getting an answer. Any help would be much appreciated.

Thanks.

 

[daon2]

Hi.

I have a problem and I'm not quite even sure what it means so I'll copy it verbatim.

Question:
Let f(x) = 3x-1, and let x_i = 2+2(i/n). Evaluate the sum of f(x_i) for i=1,...,n as a formula in terms of n.

Notes:
All I can notice is assuming n is very large then f(x_i) is approximately 5 when i=1 and equal to 11 when i=n.
In all honesty I'm not even sure what exactly I'm looking for let alone how I go about getting an answer. Any help would be much appreciated.

Thanks.

Right...

\(\displaystyle f(x_i) = 3(x_i)-1 = 3[2+2i/n]-1 = 5 + 6i/n\)

Now, you want to calculate

\(\displaystyle f(x_1)+f(x_2)+\cdots+f(x_n)\)

In doing so, you will need to know that \(\displaystyle 1+2+3+\cdots+n = \dfrac{n(n+1)}{2}\)

 

[Imum Coeli]

Thanks. Does that mean the answer is 8n+3? Or am I still not seeing it for some reason?

 

[daon2]

Thanks. Does that mean the answer is 8n+3? Or am I still not seeing it for some reason?

Yes, that is what I got as well.

 

[Imum Coeli]

Thank you so much!