Start by finding the formula, then use it to find the next two terms.
Next Two Terms: 4 and 1 Formula: a_1 = 16, a_n=a_(n-1) - 3 Explicit or Recursive? Recursive
Practice makes perfect
We want to find a formula for the given sequence.
16, 13 10, 7, ...
Notice that every term in the sequence is 3 less than the previous term. We will use this to find the formula.
a_1
a_2
a_3
a_4
...
a_n
16
13
10
7
...
—
a_1
a_1 - 3
a_2 - 3
a_3 - 3
...
a_(n-1) -3
Since the formula describes the n^(th) term using the (n-1)^\text{th} term, it is a recursive formula. Let's use it to find the next two terms.
a_n=a_(n-1) - 3
a_5=a_(5-1) - 3
a_6=a_(6 - 1) - 3
a_5=a_4 - 3
a_6=a_5 - 3
a_5=7 - 3
a_6=4 - 3
a_5=4
a_6=1
Alternative Solution
Finding an explicit formula
Alternatively, we can find an explicit formula for the sequence. To do so, notice that each term is 3 less than the previous term, with the first term 3 less than 19.
a_1
a_2
a_3
a_4
...
a_n
16
13
10
7
...
—
19 - 1*3
19 - 2*3
19 - 3*3
19 - 4* 3
...
19 - n* 3
Since the formula describes the n^(th) term using the number n, it is an explicit formula. Let's use it to find the next two terms.
