Wow, the third and fourth are hard! Especially the fourth, which is not supposed to be in Sec 1 Maths.

Give me a moment to write.

Unlike the first two questions which involve the addition or subtraction by fixed number, you will notice that each term in the third question is multiplied by 2 to get to the subsequent term.

5, 10, 20, 40, ...

We keep multiplying them by 2.

The first term is 5.
The "zero"th term is 5/2.

So, our general term is (5/2) multiplied by 2^n, where 2^n means the number of times we multiply 2 into the 5/2.

Using a similar idea for part (d), the multiplier is 2/3. But then, the signages also alternate.

To counter this, we say that the multiplier is -2/3.

The first term is 216.
The "zero"th term is 216 divided by (-2/3) which is going to be -324.

Our nth term is -324 times (-2/3)^n.

Ok thanks so much! This is really hard to understand.