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An arithmetic progression consists of an even number of terms. The sum of its odd terms is 50 whereas the sum of its even terms is 56. Find the number of terms in the series if the last term of the series exceeds the first term by 11.25.
Correct answer is '16'. Can you explain this answer?
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Verified Answer
An arithmetic progression consists of an even number of terms. The sum...
Let '2n', 'd' be the total number of terms and common difference in the series then,
By subtracting equation (1) from equation (2)
⇒ n*d = 6 ... (3)
By subtracting equation (1) from equation (2)
⇒ n*d = 6 ... (3)
It is given that T2n - T1 = 11.25
From equations (3) and(4),
From equations (3) and(4),
Hence total number of terms in the given series = 2n = 2*8 = 16.
Most Upvoted Answer
An arithmetic progression consists of an even number of terms. The sum...
Given Information:
- The arithmetic progression consists of an even number of terms.
- The sum of the odd terms is 50.
- The sum of the even terms is 56.
- The last term exceeds the first term by 11.25.
Let's solve the problem step by step:
Step 1: Finding the common difference (d)
- In an arithmetic progression, the difference between any two consecutive terms is constant and is known as the common difference.
- Let's assume the common difference as 'd'.
Step 2: Finding the number of terms (n)
- As the arithmetic progression consists of an even number of terms, let's assume the number of terms as '2n'.
- The first term is represented as 'a'.
- The last term is represented as 'a + (2n - 1)d', where 'a' is the first term and 'd' is the common difference.
Step 3: Finding the sum of the odd terms
- The sum of the odd terms can be calculated using the formula for the sum of an arithmetic series with odd terms:
- Sum of odd terms = n/2 * (2a + (n - 1)d)
- Given that the sum of the odd terms is 50, we have:
- 50 = n/2 * (2a + (n - 1)d) -- (Equation 1)
Step 4: Finding the sum of the even terms
- The sum of the even terms can be calculated using the formula for the sum of an arithmetic series with even terms:
- Sum of even terms = n/2 * (2a + (n - 2)d)
- Given that the sum of the even terms is 56, we have:
- 56 = n/2 * (2a + (n - 2)d) -- (Equation 2)
Step 5: Finding the last term
- We are given that the last term exceeds the first term by 11.25.
- Therefore, the last term (a + (2n - 1)d) - a = 11.25
- Simplifying, we get:
- (2n - 1)d = 11.25 -- (Equation 3)
Step 6: Solving the equations
- We now have three equations (Equation 1, Equation 2, and Equation 3) with three variables (a, d, and n).
- By solving these equations simultaneously, we can find the values of 'a', 'd', and 'n'.
Step 7: Solving the equations (cont.)
- Let's solve the equations using the given values:
- From Equation 1:
- 50 = n/2 * (2a + (n - 1)d)
- From Equation 2:
- 56 = n/2 * (2a + (n - 2)d)
- From Equation 3:
- (2n - 1)d = 11.25
Step 8: Solving the equations (cont.)
- Rearranging Equation
- The arithmetic progression consists of an even number of terms.
- The sum of the odd terms is 50.
- The sum of the even terms is 56.
- The last term exceeds the first term by 11.25.
Let's solve the problem step by step:
Step 1: Finding the common difference (d)
- In an arithmetic progression, the difference between any two consecutive terms is constant and is known as the common difference.
- Let's assume the common difference as 'd'.
Step 2: Finding the number of terms (n)
- As the arithmetic progression consists of an even number of terms, let's assume the number of terms as '2n'.
- The first term is represented as 'a'.
- The last term is represented as 'a + (2n - 1)d', where 'a' is the first term and 'd' is the common difference.
Step 3: Finding the sum of the odd terms
- The sum of the odd terms can be calculated using the formula for the sum of an arithmetic series with odd terms:
- Sum of odd terms = n/2 * (2a + (n - 1)d)
- Given that the sum of the odd terms is 50, we have:
- 50 = n/2 * (2a + (n - 1)d) -- (Equation 1)
Step 4: Finding the sum of the even terms
- The sum of the even terms can be calculated using the formula for the sum of an arithmetic series with even terms:
- Sum of even terms = n/2 * (2a + (n - 2)d)
- Given that the sum of the even terms is 56, we have:
- 56 = n/2 * (2a + (n - 2)d) -- (Equation 2)
Step 5: Finding the last term
- We are given that the last term exceeds the first term by 11.25.
- Therefore, the last term (a + (2n - 1)d) - a = 11.25
- Simplifying, we get:
- (2n - 1)d = 11.25 -- (Equation 3)
Step 6: Solving the equations
- We now have three equations (Equation 1, Equation 2, and Equation 3) with three variables (a, d, and n).
- By solving these equations simultaneously, we can find the values of 'a', 'd', and 'n'.
Step 7: Solving the equations (cont.)
- Let's solve the equations using the given values:
- From Equation 1:
- 50 = n/2 * (2a + (n - 1)d)
- From Equation 2:
- 56 = n/2 * (2a + (n - 2)d)
- From Equation 3:
- (2n - 1)d = 11.25
Step 8: Solving the equations (cont.)
- Rearranging Equation
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An arithmetic progression consists of an even number of terms. The sum of its odd terms is 50 whereas the sum of its even terms is 56. Find the number of terms in the series if the last term of the series exceeds the first term by 11.25.Correct answer is '16'. Can you explain this answer?
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An arithmetic progression consists of an even number of terms. The sum of its odd terms is 50 whereas the sum of its even terms is 56. Find the number of terms in the series if the last term of the series exceeds the first term by 11.25.Correct answer is '16'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about An arithmetic progression consists of an even number of terms. The sum of its odd terms is 50 whereas the sum of its even terms is 56. Find the number of terms in the series if the last term of the series exceeds the first term by 11.25.Correct answer is '16'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An arithmetic progression consists of an even number of terms. The sum of its odd terms is 50 whereas the sum of its even terms is 56. Find the number of terms in the series if the last term of the series exceeds the first term by 11.25.Correct answer is '16'. Can you explain this answer?.
An arithmetic progression consists of an even number of terms. The sum of its odd terms is 50 whereas the sum of its even terms is 56. Find the number of terms in the series if the last term of the series exceeds the first term by 11.25.Correct answer is '16'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about An arithmetic progression consists of an even number of terms. The sum of its odd terms is 50 whereas the sum of its even terms is 56. Find the number of terms in the series if the last term of the series exceeds the first term by 11.25.Correct answer is '16'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An arithmetic progression consists of an even number of terms. The sum of its odd terms is 50 whereas the sum of its even terms is 56. Find the number of terms in the series if the last term of the series exceeds the first term by 11.25.Correct answer is '16'. Can you explain this answer?.
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An arithmetic progression consists of an even number of terms. The sum of its odd terms is 50 whereas the sum of its even terms is 56. Find the number of terms in the series if the last term of the series exceeds the first term by 11.25.Correct answer is '16'. Can you explain this answer?, a detailed solution for An arithmetic progression consists of an even number of terms. The sum of its odd terms is 50 whereas the sum of its even terms is 56. Find the number of terms in the series if the last term of the series exceeds the first term by 11.25.Correct answer is '16'. Can you explain this answer? has been provided alongside types of An arithmetic progression consists of an even number of terms. The sum of its odd terms is 50 whereas the sum of its even terms is 56. Find the number of terms in the series if the last term of the series exceeds the first term by 11.25.Correct answer is '16'. Can you explain this answer? theory, EduRev gives you an
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