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if the sum between the smallest and largest of 5 consecutive odd numbers is 1 854 what is their positive difference

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If the sum between the smallest and largest of 5 consecutive odd numbers is 1,854, what is their positive difference?

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Answer to a math question If the sum between the smallest and largest of 5 consecutive odd numbers is 1,854, what is their positive difference?

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Denotemos el más pequeño de los 5 números impares consecutivos como \( x \). Como son números impares consecutivos, los otros cuatro números serían \( x + 2 \), \( x + 4 \), \( x + 6 \), y \( x + 8 \). La suma de estos cinco números se da como 1.854: \[ x + (x + 2) + (x + 4) + (x + 6) + (x + 8) = 1854 \] Combinando términos semejantes: \[ 5x + 20 = 1854 \] Restando 20 de ambos lados: \[ 5x = 1834 \] Dividiendo por 5: \[ x = 366 \] Entonces, los cinco números impares consecutivos son 366, 368, 370, 372 y 374. La diferencia positiva entre el menor y el mayor de estos números es: \[ 374 - 366 = 8 \] Por tanto, la diferencia positiva entre el menor y el mayor de los 5 números impares consecutivos es 8.

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