# arithmetic and geometric series

#### Puly Mohloai

##### New member
the sum of n terms of an arithmetic sequence is kn squared + 3n squared, where k is a real number . show that the first , second and fifth terms of the series are consecutive terms of a geometric sequence. please help me out

#### JeffM

##### Elite Member
What did you get when you wrote out the first five terms of the arithmetic sequence?

#### apple2357

##### Full Member
Would you like help with it or would you like us to do it?

If you want help take JeffM's suggestion and let us know what you get? If you don't understand what Jeff is saying say so..

#### Dr.Peterson

##### Elite Member
the sum of n terms of an arithmetic sequence is kn squared + 3n squared, where k is a real number . show that the first , second and fifth terms of the series are consecutive terms of a geometric sequence. please help me out
I wonder if you copied something incorrectly, since [imath]kn^2+3n^2[/imath] seems unlikely.

Please show us an image of the actual problem. Also, tell us what you have learned about the sum of an arithmetic series, so we can start with that.

#### Harry_the_cat

##### Elite Member
I wonder if you copied something incorrectly, since [imath]kn^2+3n^2[/imath] seems unlikely.

Please show us an image of the actual problem. Also, tell us what you have learned about the sum of an arithmetic series, so we can start with that.
@ Dr P No, I think it is correct. It does work out.

@ Puly

Have you found $$\displaystyle S_1$$? Do you realise that this will be equal to the first term $$\displaystyle t_1$$?

Have you found $$\displaystyle S_2$$? What will $$\displaystyle S_2 - S_1$$ give you?

Can you continue until you have the first 5 terms of the arithmetic sequence?