4,8,12,16,20
A geometric sequence is an ordered set of numbers such that (after the first number) the ratio between any number and its predecessor is a constant.
A quadratic sequence is when the difference between two terms changes each step. To find the formula for a quadratic sequence, one must first find the difference between the consecutive terms. Then a second difference must be found by finding the difference between the first consecutive differences.
It is an ordered set of numbers in which the difference between any member of the sequence (except the first) and its predecessor is a constant.
The sequence in the question is NOT an arithmetic sequence. In an arithmetic sequence the difference between each term and its predecessor (the term immediately before) is a constant - including the sign. It is not enough for the difference between two successive terms (in any order) to remain constant. In the above sequence, the difference is -7 for the first two intervals and then changes to +7.
In simpler terms, a geometric sequence is a sequence in which some constant (same) number multiplies every-time to give u the next number in the sequence. 2, 4, 6, 8, 10, 12 - The constant is 2 (E.g. 2 x 2 = 4) 6, 36, 216, 1296, 7776 - The constant is 6 (E.g. 6 x 6 = 36) ------------------------------------------------------------------------------------------------------------------ To figure out the constant number we just divide one number in the sequence by the one next to it on the left. E.g. 36/6 = 6 ++++ That first example, starting at 2 with a constant=2, is arithmetical not geometrical because it simply adds 2 each time. If the constant is a multiplier the series is 2, 4, 8, 16, 32, 64, ...
The first differences for a sequence Un is the set of numbers Dn = Un+1 - Un They are the set of numbers obtained by subtracting the first number from the second, the second from the third, and so on.
A geometric sequence is an ordered set of numbers such that (after the first number) the ratio between any number and its predecessor is a constant.
The expression comes from sequences. Given a sequence U1, U2, U3, ... the first differences are (U2 - U1), (U3 - U2), (U4 - U3) and so on.If you consider these as the sequence V1, V2, v3, ... then the second differences in U are the first differences in V. So the second diffs are:V2 - V1 = (U3 - U2) - (U2 - U1) = U3 - 2*U2 + U1V3 - V2 = (U4 - U3) - (U3 - U2) = U4 - 2*U3 + U2, and so on.
0,1,1,2,3,5,8,13
A quadratic sequence is when the difference between two terms changes each step. To find the formula for a quadratic sequence, one must first find the difference between the consecutive terms. Then a second difference must be found by finding the difference between the first consecutive differences.
It is an ordered set of numbers in which the difference between any member of the sequence (except the first) and its predecessor is a constant.
Some sequence words are first, second, third, then, next, after that
a sequence of a story is like what happened first, second, third etc
You take the difference between the second and first numbers.Then take the difference between the third and second numbers. If that difference is not the same then it is not an arithmetic sequence, otherwise it could be.Take the difference between the fourth and third second numbers. If that difference is not the same then it is not an arithmetic sequence, otherwise it could be.Keep checking until you think the differences are all the same.That being the case it is an arithmetic sequence.If you have a position to value rule that is linear then it is an arithmetic sequence.
In a story sequence words can be first, second, then, next, and last
It is the counter that tells you the position of the numbers in the sequence: the first, second and so on.
It is the sequence of first differences. If these are all the same (but not 0), then the original sequence is a linear arithmetic sequence. That is, a sequence whose nth term is of the form t(n) = an + b