Answer:
1st sequence: <em>a1</em> = 1, <em>r</em> = 3
2nd sequence: <em>a1</em> = 8, <em>r</em> = 1/2
3rd sequence: <em>a1</em> = 4, <em>r</em> = -4
Step-by-step explanation:
You can find <em>a1</em> simply by looking at the first element of the sequence. This gives us that <em>a1</em> is 1 in the first sequence, 8 in the second one, and 4 at the third one.
In order to find <em>r, </em>you can note that, if the nth term of the sequence is , then the following term (the (n+1)th term) is , which is obtained from the nth term by multiplying by r. This is true for any value of n, therefore
- <em>a2 = r*a1</em>
- <em>a3 = r*a2</em>
- <em>a4 = r*a3</em>
And so on. In order to obtain <em>r</em> we can observe by how much we are multiplying each term of the sequence to obtain the following one.
In the first sequence, we go from 1 to 3, then we go from 3 to 9, then we go from 9 to 27, and so on. We are multiplying each term by 3 to obtain the following one, <em>thus r = 3.</em>
In the second sequence, we go from 8 to 4, then to 2, then to 1, and so on. We are dividing by 2, or in other words, multiplying by 1/2. <em>Therefore r = 1/2.</em>
In the third sequence, we go from 4 to -16, then to 64, then to -256 and so on. In this case we multiply by a negative number, -4, which causes the sign to change when we go from one term to the next one. we conclude in this case that <em>r = -4.</em>
I hope this helps you!