Sequence and Series: If the sum of the first 3n positive integers is 150 more than the sum of the first n positive integers, then what is the sum of the first 4n positive integers?

Question

harsimran_hs4 · Answer

lets begin
1. let me what is $$\sum_{1}^{n} x = ?$$

anonymous · Answer

i dont even know what kind of quation that is

harsimran_hs4 · Answer

i `ll put it in a simple way
do you know what is 
1 + 2 + 3 + ........................+ n = ?

anonymous · Answer

would it be 1n?

harsimran_hs4 · Answer

no...
it`s n(n+1)/2

anonymous · Answer

so how'd you get that?
i used this formula: tn=a+(n-1)d

harsimran_hs4 · Answer

use Sn because i am asking you the sum of n terms not the nth term

anonymous · Answer

okay, ill use that then

harsimran_hs4 · Answer

so now all you need to do is 
S(3n) - S(n) = 150 and get n from this expression

the use the n to calculate S(4n)

anonymous · Answer

n=15

harsimran_hs4 · Answer

you need to check again...n = 6 i think

anonymous · Answer

wait, is that 5 or S?