nancylovnl1997 nancylovnl1997
  • 12-03-2022
  • Mathematics
contestada

The sum of the 6th and seventh terms in a sequence of 12 numbers with a common difference is 16. What is the Sum of the number sequence

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zsm2800 zsm2800
  • 13-03-2022

Answer:

96

Step-by-step explanation:

commom difference = d

a₆ + a₇ = 16

a₅ + a₈ = (a₆ - d) + (a₇ + d) = a₆ + a₇ = 16

a₄ + a₉ = (a₆ - 2d) + (a₇ + 2d) = a₆ + a₇ = 16

Similarly,

a₃ + a₁₀ = 16, a₂ + a₁₁ = 16, a₁ + a₁₂ = 16

so

a₁ + a₂ + ... + a₁₁ + a₁₂ = 6 x 16 = 96

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