400,000 views
43 votes
43 votes
Identify the sequence below as arithmetic, geometric, or neither. Then find the next two terms. 10, 12, 14, 16, . . .

Identify the sequence below as arithmetic, geometric, or neither. Then find the next-example-1
User Alec Gorge
by
2.4k points

1 Answer

7 votes
7 votes

We have two types of sequences to choose, it can be arithmetic or geometric (or neither). An arithmetic sequence is the one for which the next term is always equal to the previous one plus a constant ratio, while a geometric sequence is the one for which the next term is always equal to the previous one times a constant ratio.

In order to determine if it's an arithmetic sequence we need to subtract the first term from the second, and the second from the third, if the results are equal it is arithmetic.


\begin{gathered} 12-10=14-12 \\ 2=2 \end{gathered}

It is an arithmetic sequence.

In order to determine the 5th term we need to add the ratio, which is 2, to the fourth term:


a_5=16+2=18

The term a5 is 18.

Now to find the sixth term we need to add 2 to the fith term:


a_6=18+2=20

The term a6 is 20.

User Ray Jezek
by
2.6k points