Find the Pattern: Analyzing the Sequence 5,10,15,20,25,30

To solve this problem of finding the rule for the sequence $5, 10, 15, 20, 25, 30$, we will follow these steps:

• Step 1: Analyze the difference between consecutive numbers in the sequence.
• Step 2: Identify a consistent pattern or rule.
• Step 3: Compare the pattern against the given multiple-choice answers.

Now, let's work through each step:

Step 1: Calculate the difference between consecutive terms:

$10 - 5 = 5$

$15 - 10 = 5$

$20 - 15 = 5$

$25 - 20 = 5$

$30 - 25 = 5$

Step 2: We observe that the difference between each pair of successive numbers is $5$, which is consistent throughout the sequence.

Step 3: Compare this pattern with the given choices. The choice corresponding to adding 5 consistently matches our observed pattern.

Therefore, the rule for this sequence is to add 5 to each preceding number to obtain the next number in the sequence. This corresponds with choice number 2: $+5$.