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.