Find the first four terms in the
sequence 𝑎 𝑛 plus one is equal to a half of 𝑎 𝑛 minus four, where 𝑎 two is 36,
and 𝑛 is greater than or equal to one, and it’s an integer.
Now, this is a bit tricky because
we’ve been told what the second term is, but we don’t know what the first term
is. So, we’ve got to work that out. Now, the formula was telling us
that if we take a term and halve it and then subtract four, it gives us our next
term. So, for example, 𝑎 two, the second
term, is equal to a half times 𝑎 one, so a half of the first term, take away
four. But we were told that the value of
the second term was 36, so we know that 36 is equal to a half times 𝑎 one minus
four. Now, I wanna work out what 𝑎 one
is. So, if I add four to both sides of
that equation, I get 40 is equal to a half of 𝑎 one, the first term. And then, if I double both sides of
the equation, I find that the first term must have been 80.
And we can apply our recursive
formula to work out what the third term is. Remember, to find the next term, we
have to halve this term and then subtract four. So, the third term is a half of the
second term take away four. And we know what the second term
is. It’s 36. So, the third term is a half of 36
take away four. Well, half of 36 is 18. And 18 take away four is 14. And lastly, the fourth term is a
half of the third term take away four. And we’ve just worked out that the
third term is 14, which means that the fourth term turns out to be three. So, to answer our question, the
first term is 80, the second is 36, the third term is 14, and the fourth term is three.