The first term in the sequence is 2 and the common ratio is 3. What is your answer? Find the recursive formula for 5, 10, 20, 40. Our second term is nine. So if we have the term, just so we have things straight, and then we have the value, and then we have the value of the term.
This is enough information to write the explicit formula. This sounds like a lot of work. Our third term is three. Find a6, a9, and a12 for problem 4. The recursive formula for a geometric sequence is written in the form For our particular sequence, since the common ratio r is 3, we would write So once you know the common ratio in a geometric sequence you can write the recursive form for that sequence.
Given the sequence 2, 6, 18, 54. Find the explicit formula for 5, 10, 20, 40. However, we have enough information to find it. The first time we used the formula, we were working backwards from an answer and the second time we were working forward to come up with the explicit formula.
So our first term we saw is This will give us Notice how much easier it is to work with the explicit formula than with the recursive formula to find a particular term in a sequence. Negative one times is negativenegative one times negative 15 is positive So these two statements are equivalent.
Find a6, a9, and a12 for problem 8. DO NOT multiply the 2 and the 3 together. So you could say this is 15 minus six times or let me write it better this way, minus zero times six. When writing the general expression for a geometric sequence, you will not actually find a value for this.
So we went down by six, we subtracted six. So this right here isand then to figure out what 15, so we wanna figure out, we wanna figure out what 15 minus is, and this can sometimes be confusing, but the way I always process this in my head is I say that this is the exact same thing as the negative of minus So it looks like every term, you subtract six.
Now we use the formula to get Notice that writing an explicit formula always requires knowing the first term and the common ratio.
Since we already found that in our first example, we can use it here. To find the 10th term of any sequence, we would need to have an explicit formula for the sequence. This geometric sequence has a common ratio of 3, meaning that we multiply each term by 3 in order to get the next term in the sequence.
Six times nine is 54, carry the five. However, we do know two consecutive terms which means we can find the common ratio by dividing.The steps are: Find the common difference d, write the specific formula for the given sequence, and then find the term you’re looking for.
For instance, to find the general formula of an arithmetic sequence where a 4 = –23 and a 22 = 40, follow these steps.
The expression for the nth term can be determined from the formula, but there is a short cut. #T_n = d xx n +???# As soon as see that #d = 3#, you will know that the expression for the nth term with start with #T_n = 3n#.
Example Question Here is a sequence of numbers: 4, 10, 16, 22, 28 a) Write down the next two terms of the sequence. b) Write down an expression for the n th term of this sequence. c) Work out the 50 th term of the sequence.
By "the nth term" of a sequence we mean an expression that will allow us to calculate the term that is in the nth position of the sequence. For example consider the sequence. 2, 4, 6, 8, 10, The pattern is easy to see. Now that you see it you can write the nth term.
Get an answer for '`1, 3, 1, 3, 1, 3, 1` Write an expression for the apparent nth term of the sequence. (assume that n begins with 1)' and find homework help for other Math questions at eNotes.
We start by multiplying 6 times 46, since the first 4 terms are already listed. We then add the product,to the last listed term, This gives us our answer of Let a 1 represent the first term of the sequence and a n represent the nth term.
We are told that each term is two greater than.Download