Find the missing term of the following arithmetic sequence.

  
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Part 1
The missing term is
  
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1 answer

In an arithmetic sequence, the difference between consecutive terms is constant.

From the sequence provided, we have part of the sequence as: ... 2, ?, 26, ...

Let’s denote the missing term as \( x \).

Since the difference between any two consecutive terms is the same, we can express the arithmetic sequence as:

  1. From 2 to \( x \): \[ d = x - 2 \]

  2. From \( x \) to 26: \[ d = 26 - x \]

Since both differences \( d \) are equal, we set them equal to each other: \[ x - 2 = 26 - x \]

Now, we solve for \( x \): \[ x - 2 + x = 26 \] \[ 2x - 2 = 26 \] \[ 2x = 28 \] \[ x = 14 \]

Thus, the missing term is \( 14 \).

So the missing term in the sequence is: \[ \boxed{14} \]