Video: Finding Certain Terms of a Sequence given Its General and First Terms

Video Transcript

Find the first five terms of the sequence with general term 𝑇𝑚 [𝑇 𝑛] plus one equals 𝑇 𝑛 plus five, where 𝑛 is greater than or equal to one and 𝑇 one is equal to negative 13.

So we know from the question that the first term is equal to negative 13. So that’s our first term dealt with. Now let’s take a look at the second term. Well, if we take a look at the general term, we can see that term is equal to the previous term plus five. So therefore, the second term is gonna be equal to the previous term, which is term one, so negative 13 plus five. So it’s gonna be equal to negative eight. Okay, so that’s our second term dealt with.

Then, term three is gonna be equal to the previous term plus five. So that’s gonna be negative eight plus five, which gonna be equal to negative three. And then term four is gonna be equal to negative three plus five because negative three was the previous term which gonna be equal to two.

And then finally, we’ve got term five, which gonna be equal to two plus five, which gonna be equal to seven. And we’ve got two plus five because two is the previous term.

So therefore, we can say that the first five terms of the sequence with general term 𝑇𝑚 [𝑇 𝑛] plus one equals 𝑇𝑛 plus five, where 𝑛 is greater than or equal to one and 𝑇 one, the first term, is equal to negative 13, are negative 13, negative eight, negative three, two, and seven.