### Video Transcript

If π sub π is a sequence defined
as π sub one equals 11 and π sub π plus one equals π sub π minus three, where
π is greater than or equal to one, then the fourth term equals what.

Weβre given four answer options:
two, four, five, or eight. In this question, weβre given a
formula for a sequence. This type of formula is called a
recursive formula. And thatβs when the terms of a
sequence are defined using one or more previous terms. If we wanted to describe this term
in words, we would say that for any term with index π plus one, we take the term
before it β thatβs the one with index π β and we subtract three. And so if we wanted to find the
fourth term β thatβs the term with index four β that means that π plus one must be
equal to four, and so π must be three. And so the fourth term must be
equal to the third term minus three. But how do we find the third
term?

Well, the third term β thatβs the
term with index three β must happen when π plus one is three. And so π must be equal to two. So the third term is equal to the
second term minus three. Of course, we donβt know the second
term either. But youβve guessed it! Itβs going to be the first term
minus three. And this is also one of the
disadvantages of recursive formulas because we need to work out every term up to the
term that we need.

We do get a little bit of relief
here because weβre actually given the first term. π sub one is equal to 11. So now we can work forwards through
the sequence. If π sub one is equal to 11 and π
sub two is equal to π sub one minus three, then π sub two, the second term, is
equal to 11 minus three. And thatβs equal to eight. As the third term is equal to the
second term minus three, then our third term must be equal to eight minus three,
which is five. And finally then, the fourth term
is the third term minus three. And so five minus three is equal to
two. We can therefore give the answer
that the fourth term of the sequence is that given in option (A). Itβs the term two.