Identify the sequence below as arithmetic, geometric, or neither. Then find the next two terms. 15, 17, 19, 21, .
there is a common difference of 2, so ...
constant difference of 2
a = 15
d = 2
term n = a + (n-1) d
= 15 + (n-1) 2
That is not geometric !!! which would be term n = a r^(n-1)
To determine whether a sequence is arithmetic, geometric, or neither, we need to examine the differences between consecutive terms.
Let's calculate the differences:
17 - 15 = 2
19 - 17 = 2
21 - 19 = 2
The differences between consecutive terms are all equal to 2, which means the sequence is arithmetic.
To find the next term, we add the common difference (2) to the last term of the sequence:
21 + 2 = 23
Therefore, the next term is 23.
To find the second next term, we again add the common difference to the term we just found:
23 + 2 = 25
Hence, the next two terms are 23 and 25.