Question

Consider the sequence:

Answer 1

Explicit definition of the given sequence is: aₙ=2n+3

Option A is correct

Step-by-step explanation:

We are given the sequence: 5, 7, 11, 19, 35,....

and we need to find the explicit definition that defines the sequence.

We are given

a₁ = 5

the common difference between terms d = 2

So, the formula will be:

aₙ=a₁+(n-1)d

aₙ=5+(n-1)2

aₙ=5+2n-2

aₙ=2n+5-2

aₙ=2n+3

So, Explicit definition of the given sequence is: aₙ=2n+3

Option A is correct

Keywords: Explicit definition of the given sequence

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Answer 2

Answer:

$a_{n}=2^{n}+3$

Step-by-step explanation:

The given sequence is not arithmetic, it's a geometric sequence, that means the sequence is obtain using powers. The faster way to find the answer is to try options that fist with a geometric sequence. If we try the last one, we'll find that's the answer.

We need to try for n=1, n=2, n=3, n=4 and n=5:

a_{1}=2^{1}+3=5

a_{2}=2^{2}+3=4+3=7

a_{3}=2^{3}+3=8+3=11

a_{4}=2^{4}+3=16+3=19

a_{5}=2^{5}+3=32+3=35

Therefore, the right answer is the last choice, because as you can observe, it fits perfectly with the given sequence.