Answered

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Identify the kind of sequence shown: 2, 7, 14, 23, 34 ... *
O Arithmetic
O Geometric
ONeither

Sagot :

An Arithmetic sequence is constant so block that out. And geometric is by a fraction. So neither.
sqdancefan

Answer:

  (c)  Neither

Step-by-step explanation:

You want to know the kind of sequence that as terms 2, 7, 14, 23, 34, ....

Differences

The first differences of terms of this sequence are ...

  7 -2 = 5

  14 -7 = 7

  23 -14 = 9

  34 -23 = 11

These difference are not constant, so the sequence is not arithmetic.

These differences do not have a common ratio, so the sequence is not geometric.

Second differences

However, these differences do have a common difference:

  7 -5 = 2

  9 -7 = 2

  11 -9 = 2

The fact that second differences are constant means this is a polynomial sequence of second degree. It is a quadratic sequence, neither arithmetic nor geometric.

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Additional comment

The sequence is described by the quadratic equation ...

  a(n) = n² +2n -1

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