Consider the sequence:

5, 7, 11, 19,

write an explicit definition that defines the sequence:

a_n = 2n + 3

a_n = 3n + 2

a_n = 3n^2

a_n = 2^n + 3

  a_n = 2^n + 3

Step-by-step explanation:

The first differences have a geometric progression, so the explicit definition will be an exponential function. (It cannot be modeled by a linear or quadratic function.) The above answer is the only choice that is an exponential function.

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First differences are ...

  (7-5=)2, 4, 8, 16

Step-by-step explanation:

The given sequence = 5, 7, 11, 19, 35,....

Here , it cam be observe that the difference between the terms is not common but can be expressed as power of 2.

We can write the terms of the sequence as

Then , the required explicit definition that defines the sequence will be

Explanation:

If the exponent is negative, then that means we apply the reciprocal. So something like x^(-2) becomes 1/(x^2). A polynomial cannot have a variable in the denominator like this. So we can rule out choices A, B, and D. Choice C is the only thing left. It is a polynomial because the exponent is a positive whole number.