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If the last term of an A.P of 30 term is 119 and the 8 term from end ( towards the first term ) is 91 then find common difference of the A.P hence find the sum of an the term of A.P?
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If the last term of an A.P of 30 term is 119 and the 8 term from end (...
Given Data
- Last term (30th term) of A.P = 119
- 8th term from the end (23rd term) = 91
Finding the Common Difference
- Let the first term be 'a' and the common difference be 'd'.
- The formula for the nth term of an A.P is given by:
- Tn = a + (n-1)d
- For the 30th term:
- T30 = a + 29d = 119
- For the 23rd term:
- T23 = a + 22d = 91
Setting Up Equations
- We have two equations:
- 1. a + 29d = 119
- 2. a + 22d = 91
- Subtracting the second equation from the first:
- (a + 29d) - (a + 22d) = 119 - 91
- 7d = 28
- d = 4
Finding the First Term
- Substitute d back into either equation to find 'a':
- a + 22(4) = 91
- a + 88 = 91
- a = 3
Sum of the A.P.
- The sum of the first n terms (S_n) of an A.P is given by:
- S_n = n/2 * (2a + (n-1)d)
- For n = 30:
- S_30 = 30/2 * (2(3) + (30-1)(4))
- S_30 = 15 * (6 + 116)
- S_30 = 15 * 122 = 1830
Final Results
- Common Difference (d) = 4
- Sum of the 30 terms (S_30) = 1830
- Last term (30th term) of A.P = 119
- 8th term from the end (23rd term) = 91
Finding the Common Difference
- Let the first term be 'a' and the common difference be 'd'.
- The formula for the nth term of an A.P is given by:
- Tn = a + (n-1)d
- For the 30th term:
- T30 = a + 29d = 119
- For the 23rd term:
- T23 = a + 22d = 91
Setting Up Equations
- We have two equations:
- 1. a + 29d = 119
- 2. a + 22d = 91
- Subtracting the second equation from the first:
- (a + 29d) - (a + 22d) = 119 - 91
- 7d = 28
- d = 4
Finding the First Term
- Substitute d back into either equation to find 'a':
- a + 22(4) = 91
- a + 88 = 91
- a = 3
Sum of the A.P.
- The sum of the first n terms (S_n) of an A.P is given by:
- S_n = n/2 * (2a + (n-1)d)
- For n = 30:
- S_30 = 30/2 * (2(3) + (30-1)(4))
- S_30 = 15 * (6 + 116)
- S_30 = 15 * 122 = 1830
Final Results
- Common Difference (d) = 4
- Sum of the 30 terms (S_30) = 1830
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If the last term of an A.P of 30 term is 119 and the 8 term from end ( towards the first term ) is 91 then find common difference of the A.P hence find the sum of an the term of A.P?
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If the last term of an A.P of 30 term is 119 and the 8 term from end ( towards the first term ) is 91 then find common difference of the A.P hence find the sum of an the term of A.P? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If the last term of an A.P of 30 term is 119 and the 8 term from end ( towards the first term ) is 91 then find common difference of the A.P hence find the sum of an the term of A.P? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the last term of an A.P of 30 term is 119 and the 8 term from end ( towards the first term ) is 91 then find common difference of the A.P hence find the sum of an the term of A.P?.
If the last term of an A.P of 30 term is 119 and the 8 term from end ( towards the first term ) is 91 then find common difference of the A.P hence find the sum of an the term of A.P? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If the last term of an A.P of 30 term is 119 and the 8 term from end ( towards the first term ) is 91 then find common difference of the A.P hence find the sum of an the term of A.P? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the last term of an A.P of 30 term is 119 and the 8 term from end ( towards the first term ) is 91 then find common difference of the A.P hence find the sum of an the term of A.P?.
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