Answer:
21
Step-by-step explanation:
The first numbers we ever learn to count with are the ones on our fingers - 1, 2, 3, 4, and on and on and on. Wouldn't it be nice, then, if we could somehow transform this sequence into that one that's so familiar to us? If we could do that, we could find the number of terms just by looking at the last one.
Arithmetic sequences evolve predictably - we start with a specific number and continue adding another number (called the <em>common difference</em>) to one term to get the next.
Here, our common difference is 3, since 8 + 3 = 11, 14 + 3 = 17... you get the picture. If we ultimately want to get our sequence down to the counting numbers (1, 2, 3...) we should start by getting them down to the multiples of 3 (3, 6, 9...). To do that, we'll subtract 5 from each term in the sequence. This gets us from
8, 11, 14, 17, ... 68
to
3, 6, 9, 12, ... 63
From here, we'll divide each term by 3, finally giving us back a sequence of counting numbers:
1, 2, 3, 4, ... 21
Now, we can look at the last term sequence to find that there are 21 terms in it.
