Geometric sequences: how to systematically work them out using a method

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Could someone explain how to work out geometric sequences. For example: 2,4,8,16,32. The answer would be 2 to the power of n. I want to know how to systematically work this out using a method

Thanks!
 
Could someone explain how to work out geometric sequences. For example: 2,4,8,16,32. The answer would be 2 to the power of n. I want to know how to systematically work this out using a method

Thanks!

In general, the formula for a geometric sequence is an = arn-1. Here a is the first term (corresponding to n=1), and r is the "common ratio" between terms.

In your example, you can just recognize it; but using the formula, a = 2 and r = 2 (since each term is 2 times the preceding term), so the formula is \(\displaystyle 2\cdot 2^{n-1} = 2\cdot 2^n\div 2 = 2^n\) after simplifying.
 
What is the nth term? I know it gets timesed by 3 each time but I'm not sure how to write this down

You say you know that each term in the sequence is three times the previous term. That's great! Now let's see if we can use that one fact we know to discover another fact. We know the first term of the sequence is 2. That's not terribly helpful, but we'll note it down anyway. Maybe it'll come in handy for later. The second term is 6. Keeping in mind our rule of how the sequence is generated, we know that's the same as 2 * 3. Let's keep going. The third term is 6 * 3 = 18. But, hold on, we just found an expression for the second term. What happens if we plug that in? We find that the third term is (2 * 3) * 3 = 2 * (3 * 3) = 2 * 32. The fourth term is 18 * 3 = 54. Doing the same plug-n-chug as before shows that this is the same as (2 * 3​2) * 3. What's another way you can write that? Are you seeing a pattern emerging here? Can you create a similar expression for the fifth term? Does it fit your pattern?

People like to ascribe a lot of mysticism and weirdness to math, but really a great deal of math just boils down to critical thinking and pattern recognition. If you can successfully learn how to use what you know to find new information, and learn how to extrapolate patterns, that'll go a long way in just about any type of math. But most importantly, never be afraid to be wrong. If you've got a hunch, roll with it. If you think something might work, try it. Even in the worst case scenario where you fail, you'll almost always learn something and end up better off than you were before.
 
Could someone explain how to work out geometric sequences. For example: 2,4,8,16,32. The answer would be 2 to the power of n. I want to know how to systematically work this out using a method

Thanks!

If you have a minimum concept of geometric sequence then apply it: an = arn-1 Most of the geometric sequence is get solve by this formula. Hope it will help you. :)
 
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Could someone explain how to work out geometric sequences....?
There are loads of lessons available online (in addition to what is in your textbook and in your class notes): try here for "systemmatic" methodologies. ;)
 
You say you know that each term in the sequence is three times the previous term. That's great! Now let's see if we can use that one fact we know to discover another fact. We know the first term of the sequence is 2. That's not terribly helpful, but we'll note it down anyway. Maybe it'll come in handy for later. The second term is 6. Keeping in mind our rule of how the sequence is generated, we know that's the same as 2 * 3. Let's keep going. The third term is 6 * 3 = 18. But, hold on, we just found an expression for the second term. What happens if we plug that in? We find that the third term is (2 * 3) * 3 = 2 * (3 * 3) = 2 * 32. The fourth term is 18 * 3 = 54. Doing the same plug-n-chug as before shows that this is the same as (2 * 3​2) * 3. What's another way you can write that? Are you seeing a pattern emerging here? Can you create a similar expression for the fifth term? Does it fit your pattern?

People like to ascribe a lot of mysticism and weirdness to math, but really a great deal of math just boils down to critical thinking and pattern recognition. If you can successfully learn how to use what you know to find new information, and learn how to extrapolate patterns, that'll go a long way in just about any type of math. But most importantly, never be afraid to be wrong. If you've got a hunch, roll with it. If you think something might work, try it. Even in the worst case scenario where you fail, you'll almost always learn something and end up better off than you were before.

2*3 to the power of n-1?
 
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