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Let a
1
, a2, a3, a4, a5,  be a sequence of five consecutive odd numbers. Consider a new sequence of five
consecutive even numbers ending with 2a3.
If the sum of the numbers in the new sequence is 450, then a5 is
    Correct answer is '51'. Can you explain this answer?
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    Verified Answer
    Let a1, a2, a3,a4, a5, be a sequence of five consecutive odd numbers. ...
    5 consecutive odd numbers are a1 , a2 , a3 , a4 , a5.
    5 consecutive even numbers are 2a3 – 8, 2a3 – 6, 2a3 – 4, 2a3 – 2, 2a3
    Sum of these 5 numbers = 10a3 – 20 = 450
    a3 = 47 and a5 = 51.
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    Most Upvoted Answer
    Let a1, a2, a3,a4, a5, be a sequence of five consecutive odd numbers. ...
    New series numbers are even so middle term is 450÷5=90. so last term is 94 . so a3 is 94/2=47. so a5 is 51.
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    Let a1, a2, a3,a4, a5, be a sequence of five consecutive odd numbers. ...
    Given:
    - The sequence of five consecutive odd numbers is a1, a2, a3, a4, a5.
    - The new sequence of five consecutive even numbers ends with 2a3.
    - The sum of the numbers in the new sequence is 450.

    To find:
    - The value of a5.

    Approach:
    - Let's assume the five consecutive even numbers in the new sequence are b1, b2, b3, b4, b5.
    - Since the sequence is consecutive, the difference between any two consecutive terms will be the same.
    - The difference between consecutive odd numbers is 2, so the difference between consecutive even numbers will also be 2.
    - Therefore, we have b1 = a1 + 2, b2 = a2 + 2, b3 = a3 + 2, b4 = a4 + 2, and b5 = a5 + 2.

    Solution:

    Step 1: Express the sum of the new sequence in terms of a1 to a5.

    - The sum of the new sequence is given as 450.
    - Sum of the new sequence: b1 + b2 + b3 + b4 + b5 = (a1 + 2) + (a2 + 2) + (a3 + 2) + (a4 + 2) + (a5 + 2) = 5a1 + 5a2 + 10.

    Step 2: Express the sum of the new sequence in terms of a3.

    - Since the new sequence ends with 2a3, we have b5 = 2a3.
    - Substituting the values of b5 and b3 in the sum of the new sequence equation: (a1 + 2) + (a2 + 2) + (a3 + 2) + (a4 + 2) + 2a3 = 5a1 + 5a2 + 10.
    - Simplifying the equation: a1 + a2 + 3a3 + a4 + 4 = a1 + a2 + 2.
    - Canceling out the common terms: 3a3 + a4 + 4 = 2.
    - Rearranging the equation: 3a3 + a4 = -2.

    Step 3: Express a4 in terms of a3.

    - Since the given sequence consists of consecutive odd numbers, the difference between a3 and a4 is 2.
    - We can express a4 in terms of a3 as: a4 = a3 + 2.

    Step 4: Substitute the value of a4 in the equation from Step 2.

    - Substituting a4 = a3 + 2 in the equation 3a3 + a4 = -2: 3a3 + (a3 + 2) = -2.
    - Simplifying the equation: 4a3 + 2 = -2.
    - Solving for a3: 4a3 = -4, a3 = -1.

    Step 5: Find the value of a5.

    - Since a3 = -1, and a5 is the
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    Let a1, a2, a3,a4, a5, be a sequence of five consecutive odd numbers. Consider a new sequence of fiveconsecutive even numbers ending with 2a3.If the sum of the numbers in the new sequence is 450, then a5 isCorrect answer is '51'. Can you explain this answer?
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    Let a1, a2, a3,a4, a5, be a sequence of five consecutive odd numbers. Consider a new sequence of fiveconsecutive even numbers ending with 2a3.If the sum of the numbers in the new sequence is 450, then a5 isCorrect answer is '51'. 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 Let a1, a2, a3,a4, a5, be a sequence of five consecutive odd numbers. Consider a new sequence of fiveconsecutive even numbers ending with 2a3.If the sum of the numbers in the new sequence is 450, then a5 isCorrect answer is '51'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let a1, a2, a3,a4, a5, be a sequence of five consecutive odd numbers. Consider a new sequence of fiveconsecutive even numbers ending with 2a3.If the sum of the numbers in the new sequence is 450, then a5 isCorrect answer is '51'. Can you explain this answer?.
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