Answer
Verified
452.4k+ views
Hint: In this question, first of all, we will put the values of \[n = 1,2,3,4,...\] in the general term \[{a_n} = 2n + 1\] in order to get the Arithmetic progression after that take the difference between the terms of AP and the difference will be called as the common difference of the AP.
Complete step by step solution: We have been given general term of Arithmetic progression as \[{a_n} = 2n + 1\]
Now, we will put the values of \[n = 1,2,3,4,...\] in \[{a_n} = 2n + 1\] in order to get the AP.
For \[n = 1\] we get,
\[{a_1} = 2\left( 1 \right) + 1\]
\[ \Rightarrow {a_1} = 2 + 1\]
\[ \Rightarrow {a_1} = 3\]
For \[n = 2\] we get,
\[{a_2} = 2\left( 2 \right) + 1\]
\[ \Rightarrow {a_2} = 4 + 1\]
\[ \Rightarrow {a_2} = 5\]
For \[n = 3\] we get,
\[{a_3} = 2\left( 3 \right) + 1\]
\[ \Rightarrow {a_3} = 6 + 1\]
\[ \Rightarrow {a_3} = 7\]
For \[n = 4\] we get,
\[{a_4} = 2\left( 4 \right) + 1\]
\[ \Rightarrow {a_4} = 8 + 1\]
\[ \Rightarrow {a_4} = 9\]
Therefore, A.P. is \[3,5,7,9,...\]
Difference between 3 and 5 is 2.
Similarly,
Difference between 5 and 7 is 2 and
Difference between 7 and 9 is 2.
Hence, Common difference of arithmetic progression is 2.
Note: An arithmetic progression is a sequence of numbers such that the difference of any two successive members is a constant.
In an arithmetic progression the first term of a sequence is denoted by \[{a_1}\] and the difference of successive member is d which is also called as common difference since it’s common for all the successive numbers, then the nth term of sequence \[\left( {{a_n}} \right)\] is given by, \[{a_n} = {a_1} + \left( {n - 1} \right)d\].
Complete step by step solution: We have been given general term of Arithmetic progression as \[{a_n} = 2n + 1\]
Now, we will put the values of \[n = 1,2,3,4,...\] in \[{a_n} = 2n + 1\] in order to get the AP.
For \[n = 1\] we get,
\[{a_1} = 2\left( 1 \right) + 1\]
\[ \Rightarrow {a_1} = 2 + 1\]
\[ \Rightarrow {a_1} = 3\]
For \[n = 2\] we get,
\[{a_2} = 2\left( 2 \right) + 1\]
\[ \Rightarrow {a_2} = 4 + 1\]
\[ \Rightarrow {a_2} = 5\]
For \[n = 3\] we get,
\[{a_3} = 2\left( 3 \right) + 1\]
\[ \Rightarrow {a_3} = 6 + 1\]
\[ \Rightarrow {a_3} = 7\]
For \[n = 4\] we get,
\[{a_4} = 2\left( 4 \right) + 1\]
\[ \Rightarrow {a_4} = 8 + 1\]
\[ \Rightarrow {a_4} = 9\]
Therefore, A.P. is \[3,5,7,9,...\]
Difference between 3 and 5 is 2.
Similarly,
Difference between 5 and 7 is 2 and
Difference between 7 and 9 is 2.
Hence, Common difference of arithmetic progression is 2.
Note: An arithmetic progression is a sequence of numbers such that the difference of any two successive members is a constant.
In an arithmetic progression the first term of a sequence is denoted by \[{a_1}\] and the difference of successive member is d which is also called as common difference since it’s common for all the successive numbers, then the nth term of sequence \[\left( {{a_n}} \right)\] is given by, \[{a_n} = {a_1} + \left( {n - 1} \right)d\].
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE
Which are the Top 10 Largest Countries of the World?
How do you graph the function fx 4x class 9 maths CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Why is there a time difference of about 5 hours between class 10 social science CBSE