CAT 2017 Slot 2 Question Paper

Question 93

Let $$a_{1},a_{2},a_{3},a_{4},a_{5}$$ be a sequence of five consecutive odd numbers. Consider a new sequence of five consecutive even numbers ending with $$2a_{3}$$
If the sum of the numbers in the new sequence is 450, then $$a_{5}$$ is


Correct Answer: 51

Solution

Sum of the sequence of even numbers is $$2a_{3} + (2a_{3} - 2) + (2a_{3} - 4)$$ $$+ (2a_{3} - 6) + (2a_{3} - 8) = 450$$
=> $$10a_{3} - 20 = 450$$
=> $$a_{3} = 47$$
Hence $$a_{5} = 47 + 4 = 51$$

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