Question

Find the missing term of the following arithmetic sequence.
  
... 2 comma
font size decreased by 4 comma 26 comma ...
Question content area bottom
Part 1
The missing term is
  
enter your response here.

Answer 1

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:
\[
\boxed{14}
\]