I have the following question...
Consider the sequence defined by the formula $b_k=k^2$ for $k\ge2$. What is the third term in the sequence?
I have computed the values for $k=2$, $k=3$, and $k=4$ as shown below: $$b_2=2^2=4$$ $$b_3=3^2=9$$ $$b_4=4^2=16$$ However, I don't know what is considered the third term since $k\ge2$. Would it be 9 since you just plug in $k=3$, or would it be 16 since that's the third term if you start from 2 and count up? I haven't been able to find anything explaining how this works anywhere.
I finally got the answer back from my professor, and this was the explanation I was given. The third term in the sequence is $16$. The fact that $k\ge2$ doesn't change how each term in a sequence is referred to. Therefore: $$ \text{First term: } b_2=2^2=4 $$ $$ \text{Second term: } b_3=3^2=9 $$ $$ \text{Third term: } b_4=4^2=16 $$ Basically, the sequence still has a "first term" even though $k\ge2$, and it would still have a "second term" if $k\ge3$.