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

The 𝑛th term in a sequence is given by 𝑇_(𝑛 + 2) = 𝑇_(𝑛 + 1) + 𝑇_𝑛. Find the first six terms of this sequence, given that 𝑇₁ = 0 and 𝑇₂ = 1.

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Video Transcript

The 𝑛th term in a sequence is given by 𝑇 𝑛 plus two equals 𝑇 𝑛 plus one plus 𝑇 𝑛. Find the first six terms of this sequence, given that 𝑇 one is zero and 𝑇 two equals one.

We’re looking for the first six terms. We know the value of the first two terms. Term one equals zero and term two equals one. The equation is term 𝑛 plus two equals term 𝑛 plus one plus term 𝑛. That seems a little abstract. But if we plug in the numbers, we can understand what’s happening here.

In place of term 𝑛, we’ll put term one. If 𝑛 equals one, then 𝑛 plus one equals two. Term one plus term two will equal term 𝑛 plus two. Remember 𝑛 equals one. One plus two equals three. This equation is telling us that to find each term, you must add the previous two terms together.

Term three equals term one and two added together. Zero plus one equals one. Term four will be terms two and three added together. One plus one equals two. Term five will be terms three and four added together. One plus two equals three. And finally, term six will be terms four and five added together. Two plus three equals five.

The first six terms in this sequence are zero, one, one, two, three, five.

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