Question

Write the sequence with \[{n^{th}}\] term and \[{a_n} = 3 + 4n\].
A) \[7,{\text{ }}11,{\text{ }}15,{\text{ }}19,{\text{ }}....\]
B) \[7,{\text{ }}12,\;19,{\text{ }}24,{\text{ }}......\]
C) \[7,{\text{ }}11,{\text{ }}16,{\text{ }}19,{\text{ }}.....\]
D) \[7,\,{\text{ }}12,{\text{ }}17,{\text{ }}23,{\text{ }}.....\]

Answer 1

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 \[{a_n}\].