Analyzing the Number Sequence Pattern

Let's examine the given number sequence: 78, 65, 82, 69, 86, ?

We need to find the pattern or rule that governs the progression of numbers in this series. Let's look at the difference between consecutive terms:

• From 78 to 65: $65 - 78 = -13$ (a decrease of 13)
• From 65 to 82: $82 - 65 = +17$ (an increase of 17)
• From 82 to 69: $69 - 82 = -13$ (a decrease of 13)
• From 69 to 86: $86 - 69 = +17$ (an increase of 17)

Observing these differences, we can see a repeating pattern of operations:

Subtract 13, then Add 17, then Subtract 13, then Add 17, and so on.

The pattern is an alternating subtraction of 13 and addition of 17.

Calculating the Missing Number in the Series

The last number in the sequence is 86. Following the established pattern, the next operation after adding 17 (to get 86 from 69) should be subtracting 13.

So, to find the next number, we apply the subtraction of 13 to the last term, 86.

$86 - 13 = 73$

Therefore, the next number in the sequence is 73.

Verifying the Number Sequence

The complete sequence following this pattern would be:

$78 \xrightarrow{-13} 65 \xrightarrow{+17} 82 \xrightarrow{-13} 69 \xrightarrow{+17} 86 \xrightarrow{-13} 73$

This confirms that 73 is the correct number to follow 86 in the sequence according to the pattern.