why does $4n-1$ specifies index of a set?

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Hi I'm following a course on mathematical induction, and I found something that doesn't quite make sense to me

The professor gave os this statement: $$3+7+11+\cdots+(4n-1) = n(2n+1)$$

then he goes straight on to test this with $n=1$, and goes straight to $$3 = n(2n+1)$$

and in the case where $n=2$, he simply includes two numbers in the sets $$3 + 7= n(2n+1)$$ So here n is simply the amount of numbers that are included on the left side of the equal sign. But how is this the case? it seems to me that $3+7+11+\cdots+(4n-1)$ should be $3+7+11*(4n-1)$ which would just output some number

What am I not understanding?