Pay close attention to how the consecutive terms are related.
Recursive Rule: a_1 = 1, a_2 = 1, a_n=a_(n-1) - a_(n-2)
Next three terms: 0, - 1, - 1
Practice makes perfect
We want to write a recursive formula for the given sequence.
1, 1, 0, - 1, - 1, 0, 1, 1, ...
To do so we need to analyze how the consecutive terms are related. Let's find the difference between each pair of consecutive terms.
We can see above that the difference of the consecutive terms equals the next term. Therefore, to obtain the value of the term in the n^(th) position, we need to subtract two previous terms. With this information and knowing that the first term equals 1 and the second term also equals 1, we can write the recursive formula.
a_1=1, a_2 = 1 and a_n=a_(n-1) - a_(n-2)
We will write the next 3 terms of a sequence now.
ccccc
... & & ... & & ... [1.2em]
a_8- a_7&=& 1- 1 &=& 0 [1.2em]
a_9- a_8&=& 0- 1 &=& - 1 [1.2em]
a_(10)- a_9&=& - 1- 0&=& - 1
