
Write the first three terms in each of the sequence defined by the following:
1) ${a_n} = 3n + 2$
2) ${a_n} = {n^2} + 1$
Answer
485.4k+ views
Hint: The sequence of each term gives as many different values.
Our discussion for this sequence is about the first three terms only. Yet the sequence \[{a_n}\] has n number of values, when we put different values to the sequence it gives a different number.
Now, we are going to substitute positive integers for n of order \[1,2,3\] that is \[{a_1},{a_2},{a_3}\].
Complete step-by-step answer:
1) \[{a_n} = 3n + 2\]
Take n values for first three terms
So, \[n = 1,2,3\] we get
If we take \[n = 1\] ,
\[ \Rightarrow {a_1} = 3(1) + 2\]
\[ \Rightarrow {a_1} = 3 + 2\]
\[ \Rightarrow {a_1} = 5\]
If we take \[n = 2\] ,
\[ \Rightarrow {a_2} = 3(2) + 2\]
\[ \Rightarrow {a_2} = 6 + 2\]
\[ \Rightarrow {a_2} = 8\]
If we take \[n = 3\] ,
\[ \Rightarrow {a_3} = 3(3) + 2\]
\[ \Rightarrow {a_3} = 9 + 2\]
\[ \Rightarrow {a_3} = 11\]
Hence we get, \[{a_1} = 5,{a_2} = 8,{a_3} = 11\]
The first three terms for the sequence \[{a_n} = 3n + 2\] is \[5,8,11\]
2) \[{a_n} = {n^2} + 1\]
Take n values for first three terms
So, \[n = 1,2,3\]
If we take \[n = 1\]
\[ \Rightarrow {a_1} = {1^2} + 1\]
\[ \Rightarrow {a_1} = 1 + 1\]
\[ \Rightarrow {a_1} = 2\]
If we take \[n = 2\] ,
\[ \Rightarrow {a_2} = {2^2} + 1\]
\[ \Rightarrow {a_2} = 4 + 1\]
\[ \Rightarrow {a_2} = 5\]
If we take \[n = 3\] ,
\[ \Rightarrow {a_3} = {3^2} + 1\]
\[ \Rightarrow {a_3} = 9 + 1\]
\[ \Rightarrow {a_3} = 10\]
Hence we get, \[{a_1} = 2,{a_2} = 5,{a_3} = 10\]
$\therefore $The first three terms for the sequence \[{a_n} = {n^2} + 1\] is \[2,5,10\]
Note:Form the above observation in first sequence \[{a_n} = 3n + 2\]
if n is an odd number, the sequence is odd.
If n is an even number, the sequence is even.
In same way, the sequence \[{a_n} = {n^2} + 1\]
If n is an odd number, the sequence is even.
If n is an even number, the sequence is odd.
Both the sequences have n number of terms, for our convenience we take the first three terms. In some cases, they ask randomly, give value for \[n = 10\] or \[n = 20\] for the sequence, we can find that also by substitution.
Our discussion for this sequence is about the first three terms only. Yet the sequence \[{a_n}\] has n number of values, when we put different values to the sequence it gives a different number.
Now, we are going to substitute positive integers for n of order \[1,2,3\] that is \[{a_1},{a_2},{a_3}\].
Complete step-by-step answer:
1) \[{a_n} = 3n + 2\]
Take n values for first three terms
So, \[n = 1,2,3\] we get
If we take \[n = 1\] ,
\[ \Rightarrow {a_1} = 3(1) + 2\]
\[ \Rightarrow {a_1} = 3 + 2\]
\[ \Rightarrow {a_1} = 5\]
If we take \[n = 2\] ,
\[ \Rightarrow {a_2} = 3(2) + 2\]
\[ \Rightarrow {a_2} = 6 + 2\]
\[ \Rightarrow {a_2} = 8\]
If we take \[n = 3\] ,
\[ \Rightarrow {a_3} = 3(3) + 2\]
\[ \Rightarrow {a_3} = 9 + 2\]
\[ \Rightarrow {a_3} = 11\]
Hence we get, \[{a_1} = 5,{a_2} = 8,{a_3} = 11\]
The first three terms for the sequence \[{a_n} = 3n + 2\] is \[5,8,11\]
2) \[{a_n} = {n^2} + 1\]
Take n values for first three terms
So, \[n = 1,2,3\]
If we take \[n = 1\]
\[ \Rightarrow {a_1} = {1^2} + 1\]
\[ \Rightarrow {a_1} = 1 + 1\]
\[ \Rightarrow {a_1} = 2\]
If we take \[n = 2\] ,
\[ \Rightarrow {a_2} = {2^2} + 1\]
\[ \Rightarrow {a_2} = 4 + 1\]
\[ \Rightarrow {a_2} = 5\]
If we take \[n = 3\] ,
\[ \Rightarrow {a_3} = {3^2} + 1\]
\[ \Rightarrow {a_3} = 9 + 1\]
\[ \Rightarrow {a_3} = 10\]
Hence we get, \[{a_1} = 2,{a_2} = 5,{a_3} = 10\]
$\therefore $The first three terms for the sequence \[{a_n} = {n^2} + 1\] is \[2,5,10\]
Note:Form the above observation in first sequence \[{a_n} = 3n + 2\]
if n is an odd number, the sequence is odd.
If n is an even number, the sequence is even.
In same way, the sequence \[{a_n} = {n^2} + 1\]
If n is an odd number, the sequence is even.
If n is an even number, the sequence is odd.
Both the sequences have n number of terms, for our convenience we take the first three terms. In some cases, they ask randomly, give value for \[n = 10\] or \[n = 20\] for the sequence, we can find that also by substitution.
Recently Updated Pages
What percentage of the area in India is covered by class 10 social science CBSE

The area of a 6m wide road outside a garden in all class 10 maths CBSE

What is the electric flux through a cube of side 1 class 10 physics CBSE

If one root of x2 x k 0 maybe the square of the other class 10 maths CBSE

The radius and height of a cylinder are in the ratio class 10 maths CBSE

An almirah is sold for 5400 Rs after allowing a discount class 10 maths CBSE

Trending doubts
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Why is there a time difference of about 5 hours between class 10 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

What constitutes the central nervous system How are class 10 biology CBSE

Write a letter to the principal requesting him to grant class 10 english CBSE

Explain the Treaty of Vienna of 1815 class 10 social science CBSE
