hii ! for 18 (ii) the fourth line I’m not quite sure how you derived your answer

sorry the fourth line and the third line how did you get 3^n-2 and 3^n-5 ?? I’m not quite sure how you came to that conclusion !

We use the rules of indices to obtain it.

In the expression 3n times 3^(n - 3), I combined the 3 and the 3^(n - 3) together.

When you use the rules of indices to multiply such expressions, the powers get added.

In particular,

3 times 3^(n - 3)
= 3^1 times 3^(n - 3)
= 3^(1 + n - 3)
= 3^(n - 2)

Similarly, in the expression 3n (n - 1) divided by 2 times 3^(n - 6), I combined the 3 and the 3^(n - 6) together to obtain

3 times 3^(n - 6)
= 3^1 times 3^(n - 6)
= 3^(1 + n - 6)
= 3^(n - 5)

The simplification into a single power of 3 is important for this question as it helps us to simplify our result later on.