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insert five(5) arithmetic mean between 39 and -3​

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PeculiarHumango

✎ Answer:

The arithmetic means are 32, 25, 18, 11, and 4.

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✎ Step by Step Solution:

Let's first understand what are arithmetic means:

  • Arithmetic means are the terms between two given numbers in an arithmetic sequence.

Step 1:

We first express the problem as a sequence.

  • 39, _ , _ , _ , _ , _ , -3, where the arithmetic means are represented as the missing terms.

From the sequence, it is given that

  • the first term a₁ = 39, and
  • the seventh term a₇ = -3

Step 2:

We solve for the common difference d using the formula for finding the nth term.

  • aₙ = a₁ + (n - 1) d

The number of terms n = 7, so

  • a₇ = 39 + (7 - 1) d
  • -3 = 39 + 6d
  • 6d = -39 - 3
  • 6d = -42
  • d = -7

Step 3:

We solve for the arithmetic means a₂, a₃, a₄, a₅ and a₆.

We find these by adding the common difference to their preceding terms:

  • a₂ = a₁ + d = 39 + (-7) = 32
  • a₃ = a₂ + d = 32 + (-7) = 25
  • a₄ = a₃ + d = 25 + (-7) = 18
  • a₅ = a₄ + d = 18 + (-7) = 11
  • a₆ = a₅ + d = 11 + (-7) = 4

∴ The arithmetic means are 32, 25, 18, 11, and 4.

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