2. Write the recursive formula for the sequence 4, 2, 1,...

2. Write the recursive formula for the sequence 4, 2, 1, $\frac{1}{2}$, ... and use it to find the next three terms. 3. Find the explicit formula for the sequence 1, 3, 9, 27, ... and use it to find the 20th term of the sequence. 4. What is the difference between a geometric sequence and a geometric series? Give an example of each. For problems 5 and 6, find the sum of the series described. 5. $a_1 = 2$, $r = 5$, $n = 10$ 6. -2 + 6 + (-18) + ... , $n = 12$

Transcript

00:01 The first question says you have 4 .10, 25, write the recursive rule for it.

00:05 Then it says you have 4.

00:07 Negative 10, 25.

00:08 Write the explicit formula for it.

00:12 And then questions 3, 4, and 5.

00:15 You're supposed to write up terms or the recursive rule or the explicit, but it does not show any sequence defined in those.

00:25 And then the sixth question says the third term is 2.

00:28 The 9th, it's 1458.

00:30 Write the first five terms so this first one writing the recursive rule for this you'd say a1 is equal to four a n is what's happening to get from there to there and there to there if you add six and then try to add six again you don't hit each of the numbers that he gets you ten but ten would have be sixteen and that's not sixteen so it's not adding let's try multiplying so ten divided by four words is equal to 2 .5.

01:02 And if you take 10 times 2 .5, so we are multiplying by 2 .5 here, so that would be 2 .5 times a to the n -1, or n is greater than equal to 2.

01:22 If you want to write that as an explicit formula, that would be 2 .5, no.

01:29 It would be 4 times 5 to the n minus 1.

01:38 And you have to use n -1 as your exponent, because if you use this is the first term.

01:43 So if you put a 1 in for n minus 1, 1 minus 1 is 0 and 2 .5 to the 0 is 1 and 1 times 4 is 4.

01:54 If you were to write this as your explicit formula and you put a 1 in here, while 2 .5 of the first is 2 .5 and times 4 is 10.

02:07 So this does not give you the first term when you substitute a 1 in.

02:11 So that's why you have to use n -1 .2.

02:15 One said to write the explicit formula for this.

02:17 Now we're taking a negative 10 divided by 4 to the negative 2 .5.

02:23 And if you take negative 10 times a negative 2 .5, you'll get a positive 25.

02:30 So this explicit formula would be times a negative 2 point to the n minus 1...

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