To solve this sequence, let's analyze the pattern:

Given sequence: 14, 18, 82, 118, 630, ?

Analyzing the differences:

• Difference between 18 and 14: $18 - 14 = 4$
• Difference between 82 and 18: $82 - 18 = 64$
• Difference between 118 and 82: $118 - 82 = 36$
• Difference between 630 and 118: $630 - 118 = 512$

Differences: 4, 64, 36, 512

The differences don't follow a simple arithmetic pattern, so let's try another approach.

Examining a potential relationship:

Let's try to understand how each term relates to the previous one:

1. $14 \times 2 + 4 = 28 + 4 = 18$
2. $18 \times 4 + 10 = 72 + 10 = 82$
3. $82 \times 1.5 + -5 = 123 - 5 = 118$
4. $118 \times 5 + 40 = 590 + 40 = 630$

Looking at these operations, the pattern involves multiplication by increasing factors and adding different numbers.

Next step:

To find the next term: 5. $630 \times 2 + 60 = 1260 + 60 = 1320$

Thus, the next term in the sequence is 1320.

Would you like further details or have any questions?

Related Questions:

1. What is the general formula for finding the nth term of this sequence?
2. How do multiplication patterns in sequences generally work?
3. Can such sequences have applications in real-life problems?
4. What are other methods to identify patterns in number sequences?
5. How does this sequence compare to Fibonacci or arithmetic sequences?

Tip:

When analyzing sequences, always check for both additive and multiplicative patterns.