What type of sequence is this?
2 , 3, 5, 8, 12
Arithmetic, geometric or neither
it definitely not an arithemetic progression nor a geometric progression
take the come difference of an
Ap and the ratio of a G.P
Ap=3-2=1
gp=3/2
Ap=5-3=2
Gp=5/3
does it make any sense.....aren't they supose to yield the same result?????.
Neither arithmetic nor geometric,
but there is a nice pattern.
We can write it as a recursive formula.
term(n) = term(n-1) + n, n>1, term(1) = 2
Neither. Each number in the sequence is obtained by adding 1,2,3,4. So,
2 + 1 = 3
3 + 2 = 5
5 + 3 = 8
8 + 4 = 12
To determine the type of sequence, we need to check if there is a common difference between consecutive terms (arithmetic sequence) or if there is a common ratio between consecutive terms (geometric sequence).
To check for an arithmetic sequence, we look for a consistent difference between the terms. Let's find the differences between the consecutive terms:
3 - 2 = 1
5 - 3 = 2
8 - 5 = 3
12 - 8 = 4
The differences are not constant, so it is not an arithmetic sequence.
Now let's check for a geometric sequence by calculating the ratios between consecutive terms:
3 / 2 = 1.5
5 / 3 ≈ 1.67
8 / 5 = 1.6
12 / 8 = 1.5
The ratios are not constant either, so it is not a geometric sequence.
Therefore, based on the given terms, the sequence 2, 3, 5, 8, 12 is neither an arithmetic nor a geometric sequence.