When you're learning about geometric sequences, there are some common mistakes that can trip you up. Here are some things to be careful about:
Getting the Formulas Mixed Up: There are two important formulas. The first one is called the explicit formula: ( a_n = a_1 \cdot r^{(n - 1)} ).
The second one is the recursive formula: ( a_n = a_{n - 1} \cdot r ).
It's important to know which one to use when!
Using the Wrong Starting Point: A lot of students forget that the first term in a sequence starts with ( n = 1 ). Make sure you check your starting points!
Mixing Up Multiplication and Addition: In geometric sequences, you multiply by ( r ).
But in arithmetic sequences, you add. If you mix these up, you'll get the wrong answers!
Not Paying Attention to the Common Ratio: The common ratio, ( r ), is super important. If you make even a small mistake in finding it, it can cause big problems later.
Stay focused, and you’ll get the hang of these formulas really quickly!
When you're learning about geometric sequences, there are some common mistakes that can trip you up. Here are some things to be careful about:
Getting the Formulas Mixed Up: There are two important formulas. The first one is called the explicit formula: ( a_n = a_1 \cdot r^{(n - 1)} ).
The second one is the recursive formula: ( a_n = a_{n - 1} \cdot r ).
It's important to know which one to use when!
Using the Wrong Starting Point: A lot of students forget that the first term in a sequence starts with ( n = 1 ). Make sure you check your starting points!
Mixing Up Multiplication and Addition: In geometric sequences, you multiply by ( r ).
But in arithmetic sequences, you add. If you mix these up, you'll get the wrong answers!
Not Paying Attention to the Common Ratio: The common ratio, ( r ), is super important. If you make even a small mistake in finding it, it can cause big problems later.
Stay focused, and you’ll get the hang of these formulas really quickly!