Find the ${10^{th}}$ term of A.P. 2,7,12,.......
Answer
Verified
506.7k+ views
Hint: Find Common difference and then use formula for nth term of an A.P.
We have been given A.P. : 2,7,12,.......
As we know that A.P. or Arithmetic Progression is a sequence of numbers with a common difference between all consecutive terms.
So, let nth term of A.P. be ${A_n}$
So, the given terms are ${A_1},{A_2},{A_3},.....{A_n}$
$ \Rightarrow {A_1} = 2,{A_2} = 7,{A_3} = 12 $
Let common difference be $d$
So we can say that,
${A_2} - {A_1} = {A_3} - {A_2} = d$
$ \Rightarrow d = 7 - 2 = 5$
Now, as we know that ${a_n} = a + \left( {n - 1} \right)d$
Here $n = 10$ and $a = {A_1} = 2$
$ \Rightarrow {A_{10}} = 2 + \left( {10 - 1} \right)5$
$ \Rightarrow {A_{10}} = 2 + \left( {9 \times 5} \right)$
$ \Rightarrow {A_{10}} = 2 + 45$
$\therefore {A_{10}} = 47$
Note: In these types of questions we firstly find the common difference using any two consecutive terms and then use the formula to find nth term of an A.P. Here we put the values of first term, common difference and n in the equation and get our answer
We have been given A.P. : 2,7,12,.......
As we know that A.P. or Arithmetic Progression is a sequence of numbers with a common difference between all consecutive terms.
So, let nth term of A.P. be ${A_n}$
So, the given terms are ${A_1},{A_2},{A_3},.....{A_n}$
$ \Rightarrow {A_1} = 2,{A_2} = 7,{A_3} = 12 $
Let common difference be $d$
So we can say that,
${A_2} - {A_1} = {A_3} - {A_2} = d$
$ \Rightarrow d = 7 - 2 = 5$
Now, as we know that ${a_n} = a + \left( {n - 1} \right)d$
Here $n = 10$ and $a = {A_1} = 2$
$ \Rightarrow {A_{10}} = 2 + \left( {10 - 1} \right)5$
$ \Rightarrow {A_{10}} = 2 + \left( {9 \times 5} \right)$
$ \Rightarrow {A_{10}} = 2 + 45$
$\therefore {A_{10}} = 47$
Note: In these types of questions we firstly find the common difference using any two consecutive terms and then use the formula to find nth term of an A.P. Here we put the values of first term, common difference and n in the equation and get our answer
Recently Updated Pages
Class 10 Question and Answer - Your Ultimate Solutions Guide
Master Class 10 Science: Engaging Questions & Answers for Success
Master Class 10 Maths: Engaging Questions & Answers for Success
Master Class 10 General Knowledge: Engaging Questions & Answers for Success
Master Class 10 Social Science: Engaging Questions & Answers for Success
Master Class 10 English: Engaging Questions & Answers for Success
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
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
A Paragraph on Pollution in about 100-150 Words