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**Hint:**In this question we have to find the sequence with \[{n^{th}}\] term and \[{a_n} = 3 + 4n\].

The expression \[{({a_n})_{n \in N}}\] denotes a sequence whose \[{n^{th}}\] element is given by the variable \[{a_n}\].

The \[{n^{th}}\] element of the sequence is given.Therefore we can get the \[{1^{st}},{\text{ }}{2^{nd}},\,{\text{ }}{3^{rd}},\,\;{4^{th}},\;\;....\] elements of the sequence respectively by putting the value of \[n = 1,{\text{ }}2,{\text{ }}3,{\text{ }}4,{\text{ }}.....\] in the expression \[{a_n}\].

**Complete step-by-step answer:**

It is given that the \[{n^{th}}\] term of the sequence is \[{a_n} = 3 + 4n\].

We need to find out the elements of the sequence.

By putting the value of \[n = 1,{\text{ }}2,{\text{ }}3,{\text{ }}4,\,{\text{ }}.....\] in the expression \[{a_n}\], we will get the \[{1^{st}},\;{\text{ }}{2^{nd}},\,{\text{ }}{3^{rd}},{\text{ }}{4^{th}},\,\,....\] terms of the sequence respectively.

Putting the value of \[n = 1\] in \[{a_n}\] we get,

The first term of the sequence, \[{a_1} = 3 + 4 \times 1 = 3 + 4 = 7\]

Putting the value of \[n = 2\] in \[{a_n}\] we get,

The second term of the sequence, \[{a_2} = 3 + 4 \times 2 = 3 + 8 = 11\]

Putting the value of \[n = 3\] in \[{a_n}\] we get,

The third term of the sequence, \[{a_3} = 3 + 4 \times 3 = 3 + 12 = 15\]

Putting the value of \[n = 4\] in \[{a_n}\] we get,

The fourth term of the sequence, \[{a_4} = 3 + 4 \times 4 = 3 + 16 = 19\]

Similarly we can find all the elements of the sequence.

Thus we get, the elements of the sequence are, \[7,{\text{ }}11,\;{\text{ }}15,\;\;19,\;.....\]

Hence we get, the sequence with \[{n^{th}}\] term \[{a_n} = 3 + 4n\] is \[7,{\text{ }}11,\;{\text{ }}15,\;\;19,\;.....\] .

**So, the correct answer is “Option A”.**

**Note:**In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters. Like a set, it contains members. The number of elements is called the length of the sequence.

The expression \[{({a_n})_{n \in N}}\] denotes a sequence whose \[{n^{th}}\] element is given by the variable \[{a_n}\].

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