Question Video: Finding the Next Four Terms in a Sequence given Its General Formula and Second Term Mathematics • 9th Grade

Video Transcript

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.