Indicate whether the sequence is arithmetic, geometric or neither 10,12,22,32,42.....
You are adding 10 to each previous value. What would that indicate to you?
indicate whether or not each sequence is arithmetic. and write an expression for the general term.
5,7,9,11,...
1,3,9,27,...
75,65,55,45,...
To determine whether the given sequence is arithmetic, geometric, or neither, we need to examine the pattern between consecutive terms.
An arithmetic sequence is a sequence in which the difference between any two consecutive terms is constant. In other words, if you subtract any term from its previous term, you will always get the same value.
A geometric sequence, on the other hand, is a sequence in which the ratio between any two consecutive terms is constant. In other words, if you divide any term by its previous term, you will always get the same value.
Let's examine the given sequence:
10, 12, 22, 32, 42...
By calculating the differences between consecutive terms, we can determine if it is arithmetic:
12 - 10 = 2
22 - 12 = 10
32 - 22 = 10
42 - 32 = 10
The differences between consecutive terms are not constant, so the sequence is not arithmetic.
Now, let's calculate the ratios between consecutive terms to check if it is geometric:
12 / 10 = 1.2
22 / 12 ≈ 1.83
32 / 22 ≈ 1.45
42 / 32 ≈ 1.31
The ratios between consecutive terms are not constant either, so the sequence is not geometric.
Since the differences and ratios between consecutive terms are not constant, the given sequence is neither arithmetic nor geometric.