Find The Sum Of Series 1 3 5 7 9 Up To N Terms Class 10 Maths CBSE

CoursesCourses for KidsFree study materialOffline CentresMoreStore

Talk to our experts

1800-120-456-456

Sign In

• Question Answer

• Class 10

• Maths

• Find the sum of series 1 3 5 7...

AnswerQuestion Answers for Class 12Class 12 BiologyClass 12 ChemistryClass 12 EnglishClass 12 MathsClass 12 PhysicsClass 12 Social ScienceClass 12 Business StudiesClass 12 EconomicsQuestion Answers for Class 11Class 11 EconomicsClass 11 Computer ScienceClass 11 BiologyClass 11 ChemistryClass 11 EnglishClass 11 MathsClass 11 PhysicsClass 11 Social ScienceClass 11 AccountancyClass 11 Business StudiesQuestion Answers for Class 10Class 10 ScienceClass 10 EnglishClass 10 MathsClass 10 Social ScienceClass 10 General KnowledgeQuestion Answers for Class 9Class 9 General KnowledgeClass 9 ScienceClass 9 EnglishClass 9 MathsClass 9 Social ScienceQuestion Answers for Class 8Class 8 ScienceClass 8 EnglishClass 8 MathsClass 8 Social ScienceQuestion Answers for Class 7Class 7 ScienceClass 7 EnglishClass 7 MathsClass 7 Social ScienceQuestion Answers for Class 6Class 6 ScienceClass 6 EnglishClass 6 MathsClass 6 Social ScienceQuestion Answers for Class 5Class 5 ScienceClass 5 EnglishClass 5 MathsClass 5 Social ScienceQuestion Answers for Class 4Class 4 ScienceClass 4 EnglishClass 4 MathsFind the sum of series 1, 3, 5, 7, 9,…… up to n terms?AnswerVerified519.3k+ viewsHint: We can see that the given series in the problem follows an Arithmetic Progression (AP). We find the ${{n}^{th}}$ term of the series by using the first term and common difference of the given series. Once, we find the ${{n}^{th}}$ terms, we use the sum of n terms of Arithmetic Progression (AP) to get the desired result.Complete step-by-step solution:According to the problem, we have a series given as 1, 3, 5, 7, 9,……. We need to find the sum of the elements in this series up to n terms.We know that an Arithmetic Progression (AP) is of form a, a+d, a+2d,…….., where ‘a’ is known as the first term and ‘d’ is known as common difference.We can see that the difference between any two consecutive numbers is 2. We can see that the given series are in AP (Arithmetic Progression) with the first term ‘1’ and common difference ‘2’.Let us find the ${{n}^{th}}$ term for the given series. We know that ${{n}^{th}}$ term of an Arithmetic Progression (AP) is defined as ${{T}_{n}}=a+\left( n-1 \right)d$.So, we have ${{n}^{th}}$ term for the given series as ${{T}_{n}}=1+\left( n-1 \right)2$.${{T}_{n}}=1+2n-2$.${{T}_{n}}=2n-1$ ---(1).Now let us find the sum of n terms of the given series. We know that sum of n terms of an Arithmetic Progression (AP) is defined as ${{S}_{n}}=\dfrac{n}{2}\times \left( a+{{T}_{n}} \right)$.So, we have sum of n terms of the given series as ${{S}_{n}}=\dfrac{n}{2}\times \left( 1+2n-1 \right)$.${{S}_{n}}=\dfrac{n}{2}\times \left( 2n \right)$.${{S}_{n}}=n\times n$.${{S}_{n}}={{n}^{2}}$.We have found the sum of n terms of the series 1, 3, 5, 7, …… is ${{n}^{2}}$.$\therefore$ The sum of series 1, 3, 5, 7, 9,…… up to n terms is ${{n}^{2}}$.Note: We can also use the sum of ‘n’ natural numbers to find the sum of the given series after calculating the ${{n}^{th}}$ term. Whenever we see a problem following Arithmetic Progression (AP), we make use of ${{n}^{th}}$ term. Similarly, we can expect problems to find the sum of even numbers up to n-terms.Recently Updated PagesMaster Class 10 Computer Science: Engaging Questions & Answers for SuccessMaster Class 10 English: Engaging Questions & Answers for SuccessMaster Class 10 Social Science: Engaging Questions & Answers for SuccessMaster Class 10 General Knowledge: Engaging Questions & Answers for SuccessMaster Class 10 Maths: Engaging Questions & Answers for SuccessMaster Class 10 Science: Engaging Questions & Answers for SuccessMaster Class 10 Computer Science: Engaging Questions & Answers for SuccessMaster Class 10 English: Engaging Questions & Answers for SuccessMaster Class 10 Social Science: Engaging Questions & Answers for SuccessMaster Class 10 General Knowledge: Engaging Questions & Answers for SuccessMaster Class 10 Maths: Engaging Questions & Answers for SuccessMaster Class 10 Science: Engaging Questions & Answers for Success

• 1
• 2

Trending doubtsWhy is there a time difference of about 5 hours between class 10 social science CBSEWho Won 36 Oscar Awards? Record Holder RevealedWhat is the median of the first 10 natural numbers class 10 maths CBSEWrite a letter to the principal requesting him to grant class 10 english CBSEWho is the executive head of the government APresident class 10 social science CBSEThe Equation xxx + 2 is Satisfied when x is Equal to Class 10 MathsWhy is there a time difference of about 5 hours between class 10 social science CBSEWho Won 36 Oscar Awards? Record Holder RevealedWhat is the median of the first 10 natural numbers class 10 maths CBSEWrite a letter to the principal requesting him to grant class 10 english CBSEWho is the executive head of the government APresident class 10 social science CBSEThe Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

• 1
• 2