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How many terms are there in A.P with first term -14 Nad fifth term 2 and the last term is 62 and sum of all terms is 62?
Most Upvoted Answer
How many terms are there in A.P with first term -14 Nad fifth term 2 a...
Given information:
- First term (a) = -14
- Fifth term = 2
- Last term = 62
- Sum of all terms = 62
Finding the common difference (d):
- The formula for the nth term of an arithmetic progression (A.P) is: \(a_n = a + (n-1)d\)
- Substitute the values of the first term and the fifth term into the formula to find the common difference:
\(2 = -14 + 4d\)
\(4d = 16\)
\(d = 4\)
Finding the number of terms in the A.P:
- The last term of an A.P is given by: \(a_n = a + (n-1)d\)
- Substitute the values of the last term and the common difference into the formula to find the number of terms:
\(62 = -14 + (n-1)4\)
\(n-1 = 19\)
\(n = 20\)
Explanation:
- The common difference of the A.P is 4.
- The number of terms in the A.P is 20.
- Therefore, there are 20 terms in the A.P with the given conditions.
- First term (a) = -14
- Fifth term = 2
- Last term = 62
- Sum of all terms = 62
Finding the common difference (d):
- The formula for the nth term of an arithmetic progression (A.P) is: \(a_n = a + (n-1)d\)
- Substitute the values of the first term and the fifth term into the formula to find the common difference:
\(2 = -14 + 4d\)
\(4d = 16\)
\(d = 4\)
Finding the number of terms in the A.P:
- The last term of an A.P is given by: \(a_n = a + (n-1)d\)
- Substitute the values of the last term and the common difference into the formula to find the number of terms:
\(62 = -14 + (n-1)4\)
\(n-1 = 19\)
\(n = 20\)
Explanation:
- The common difference of the A.P is 4.
- The number of terms in the A.P is 20.
- Therefore, there are 20 terms in the A.P with the given conditions.
Community Answer
How many terms are there in A.P with first term -14 Nad fifth term 2 a...
20
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How many terms are there in A.P with first term -14 Nad fifth term 2 and the last term is 62 and sum of all terms is 62?
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How many terms are there in A.P with first term -14 Nad fifth term 2 and the last term is 62 and sum of all terms is 62? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about How many terms are there in A.P with first term -14 Nad fifth term 2 and the last term is 62 and sum of all terms is 62? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for How many terms are there in A.P with first term -14 Nad fifth term 2 and the last term is 62 and sum of all terms is 62?.
How many terms are there in A.P with first term -14 Nad fifth term 2 and the last term is 62 and sum of all terms is 62? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about How many terms are there in A.P with first term -14 Nad fifth term 2 and the last term is 62 and sum of all terms is 62? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for How many terms are there in A.P with first term -14 Nad fifth term 2 and the last term is 62 and sum of all terms is 62?.
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