Five Consecutive Odd and Even Sequences

Question

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

Accepted Answer

51. Let the 5 consecutive even numbers ending with $2a_3$ be: $2a_3 - 8, 2a_3 - 6, 2a_3 - 4, 2a_3 - 2, 2a_3$. Their sum = $10a_3 - 20$. Given sum = 450: $$10a_3 - 20 = 450 \implies 10a_3 = 470 \implies a_3 = 47$$ Since $a_1, a_2, a_3, a_4, a_5$ are consecutive odd numbers: $a_5 = a_3 + 4 = 47 + 4 = 51$.

Answer

No other option is correct for this question.

Five Consecutive Odd and Even Sequences

Explanation

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