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9 votes
9 votes
Identify the kind of sequence shown: 2, 7, 14, 23, 34 ... *

O Arithmetic
O Geometric
ONeither

User Smerlung
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2 Answers

21 votes
21 votes
An Arithmetic sequence is constant so block that out. And geometric is by a fraction. So neither.
User Ezio
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20 votes
20 votes

Answer:

(c) Neither

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

User Prajwal Gonsalves
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