Let a1, 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
Explanation:
Since 2a3 is the highest number in the new sequence, the sequence of 5 even numbers starting with the lowest, when expressed (in terms of a3) is (2a3 - 8), (2a3 - 6), (2a3 - 4), (2a3 - 2), 2a3
Sum of these 5 numbers = 450
⇒ 2a3 - 8 + 2a3 - 6 + 2a3 - 4 + 2a3 - 2 + 2a3 = 450 ⇒ 10a3 – 20 = 450 ⇒ 10a3 = 470 ⇒ a3 = 47
Now in the original sequence of 5 odd numbers, a3 = 47 ⇒ a5 = a3 + 4 ⇒ a5 = 47 + 4 = 51
Hence, 51.
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