Understanding Arithmetic Sequences
Arithmetic sequences are simply ordered lists of numbers where you add or subtract the same value every time. For example, in the sequence 3, 7, 11, 15, you're adding 4 each time - that's your common difference (d).
The magic formula aₙ = a₁ + n−1d helps you find any term in the sequence. Here, a₁ is your first term, n is the position you want, and d is your common difference. Master this formula and you'll solve most arithmetic sequence problems!
Finding the common difference is straightforward - just subtract any term from the next term. In the example 66, ?, 78, you can work backwards: 78 = 66 + 2d, so d = 6.
Pro Tip: When sequences decrease (like 20, 17, 14, 11), your common difference will be negative!
Arithmetic means are the missing terms between two known terms. Use the simple formula M = a+b/2 for one missing term, or the main formula for multiple missing terms. Once you find the common difference, just keep adding it to fill in the gaps!