Questions:
1. Give an example of a geometric sequence.
2. What is the first term?
3. What is the common ration?
4. What is the 10th term of the geometric sequence?
5. How will you determine the nth term of a geometric sequence
"Write a story about your geometric sequence"
Answers:
1.)Example 1: {2,6,18,54,162,486,1458,...}
2.)For geometric sequences, the common ratio is r, and the first term a1 is often referred to simply as "a". Since we get the next term by multiplying by the common ratio, the value of a2 is just: a2 = ar. Continuing, the third term is: a3 = r(ar) = ar2.
3.)The common ratio is the number you multiply or divide by at each stage of the sequence. The common ratio is therefore 2. You can find out the next term in the sequence by multiplying the last term by 2.
4.)So, the given sequence represents the geometric progression. The 10th term of the sequence will be given by ar9 a r 9 .
5.)Solution: To find a specific term of an arithmetic sequence, we use the formula for finding the nth term. Step 1: The nth term of an arithmetic sequence is given by an = a + (n – 1)d. So, to find the nth term, substitute the given values a = 2 and d = 3 into the formula.
"Write a story about your geometric sequence"
Answer:
A ball bouncing is an example of a finite geometric sequence. Each time the ball bounces it's height gets cut down by half. If the ball's first height is 4 feet, the next time it bounces it's highest bounce will be at 2 feet, then 1, then 6 inches and so on, until the ball stops bouncing
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