Pay close attention to how the consecutive terms are related.
a_1=1 and a_n=a_(n-1) +3
Practice makes perfect
We want to write a recursive formula for the given sequence.
1, 4, 7, 10, ...To do so we need to analyze how the consecutive terms are related. Let's find the difference between each pair of consecutive terms.
ccccc
a_2-a_1&=& 4-1 &=& 3 [1.2em]
a_3-a_2&=& 7-4 &=& 3 [1.2em]
a_4-a_3&=& 11-7&=& 3 [1.2em]
... & & ... & & ...
a_n-a_(n-1) = 3
We can see above that the difference between the consecutive terms equals 3. Therefore, to obtain the value of the term in the n^(th) position, we need to add 3 to the previous term. With this information and knowing that the first term equals 1, we can write the recursive formula.
a_1=1 and a_n=a_(n-1) +3
