Sequence question? (algebra II) 10 pts?!?!?
Which is the 19th term in the sequence: a_n = -2(n - 3)? 19 32 32 44 Which represents the second term of the sequence: a_1 = 10 and a_n = 0.5(a_n-1)? 20 15 2 5 Which represent the first three terms of the sequence: a_1 = 2 and a_n = 3(a_n-1)^2? 2, 12, 27 3, 12, 27 2, 12, 432 3, 12, 432
Algebra II sequences help? (10 points)?
1. Use the iterative rule to find the seventh term of the sequence: a_n = 3^n – 1. 728 2186 729 2187 2. Find the common ratio of the sequence: 320, 80, 20, 5, 1.25, … Option A: 40 Option B: 1/40 Option C: 4 Option D: 1/4 3. Find the next term of the sequence: 1/28, -1/16, 1/2, -4, 32 -256 -512 256 512 4. Which is the 11th term in the sequence: 1/2, 1, 2, 4, 8 102 256 512 1024
Algebra II a few questions? (sequence)?
Which is the common difference of the sequence: -92, -74, -56, -38, -20, …? -19 -18 19 18 Use the iterative rule to find the eighth term in the sequence a_n = 25 − 3n. 8 176 1 49 Which is the iterative rule for the sequence: 15.5, 13, 10.5, 8, 5.5, 3, …? a_n = 18 2.5n a_n = 15.5 − 2.5n a_n = 18 + 2.5n a_n = 15.5 + 2.5n Which is the iterative rule for the sequence: 2, 9, 16, 23, 30, …? a_n = 2 + 7n a_n = 5 + 7n a_n = 5 7n a_n = 2 7n
Series and Sequence question? (Algebra II)?
the sum of an arithmetic series is (n / 2) [2a + (n - 1) d] a is the first number (6) n is the number of terms (26) d is the difference (8) the sum of the first 26 terms is (26/2) [ 2(6) + 25 (8)] 13 [ 12 + 200 ] 13 x 212 = 2756
Algebra II help? Arithmetic sequences?
Just in case, I'll go over the basics: Okay, so an arithmetic sequence is basically like a simple pattern. The difference between each number is the same. This difference is called "d" in your format. First, let's break apart your format: an = the number you're trying to find. "n" is the term of a number in the pattern. Like 1st number, 5th number, nth number etc... a1 = the first number in the pattern. d = difference between each number For example, take this pattern: 3, 6, 9, 12. a1 = 3, d = 3 In this example: 12, 9, 6, 3. a1 = 12, d = -3. ______________________________________... Okay, let's tackle those problems. On day 3, a3 = 13. On day 20, a20 = 64. First, we need to find the difference. Since they give us two numbers that aren't next to each other, we'll have to find the difference between the two numbers and divide it by the number of terms between the two numbers. Wow, sorry that sounds confusing. It's like this: Difference between a20 and a3 = 64 - 13 = 51 Number of terms between a20 and 3 = 20 - 3 = 17 Difference between each number = 51 / 17 = 3 Now, we need to find a1. To get from a3 to a1, subtract 2 times the difference. a3 = 13 a2 = 13 - 3 = 10 a1 = 10 - 3 = 7 Or you can just do 13 - 2(3) = 7. And the rest should be easy. Just use the format: a.) a12 = 7 + (12 - 1)3 = 7 + 3(11) = 40 b.) a50 = 7 + (50 - 1)3 = 7 + 3(49) = 154 Voila! :D
Algebra II questions, help hopefully?
The problem that I have with anyone asking 10 questions and some of them so straight forward is that I don't believe that you have even tried to answer them. Therefore I am going to help you, but I am not going to give you the answers. 1. A geometric sequence is where each separate term is the previous term multiplied by the same "common ratio" or amount. -18 x -2/3 = 12 12 x -2/3 = -8 Therefore does -8 x -2/3 = 5? If it does then YES it is a geometric sequence, if it doesn't then NO it is not. 2. 1 * ? = 5 5* -5 = -25 -25 * -5 = 125 Therefore is the ? equal to -5. If yes it is a geometric sequence, if not then NO. 3. The pattern is that the common ratio = 2 20 x 2 = 40, 40 x 2 = 80, 80 x 2 = 160, 160 x 2 = ? etc etc 4. 20 * r = 40. and 40 *r = 80. Well what is "r"? 5. t4 = 48 t5 = 48 * r t6 = t5 * r = 48*r*r = 48*r^2 But we know that t6 = 192 Therefore 48r^2 = 192 r^2 = 192/48 = 4 r = sqrt 4 = plus or minus 2 As you require the 8th term this is t6 *r^2 = 192 * 4 =? It makes no difference whether r is +2 or -2 as r^2 = 4 in both scenarios 6. t1 = 5 t2 = 5 * -1/2 = -5/2 t3 = -5/2 * -1/2 = +5/4 t4 = +5/4 *-1/2 = -5/8 t5 = =5/8 * -1/2 = +5/16 Therefore t6 = what? 7. The sum of the first 8 terms. The common ration is 1/4. Each term is a quarter of the one preceding it You are given 256 + 64 +16 + 4 (then the next 4 are) 1 + 1/4 + 1/16 + 1/64 Add them up = ?? 8. The common ratio is -2 The first 8 terms are +3 - 6 + 12 -24 +48 - 96 + 192 - 384 Add them up! 9. The common ratio is 1.4. Notice that in numerical terms the differences between each two numbers are getting bigger as you go through the sequence. Therefore do you think that this sequence will converge? NO - therefore a) it does not exist 10. Now bearing in mind what I have just advised for number 9, what do you think is the answer for number 10?
Algebra II: Sequences and Series Help? 10 points!?
10. What are the next 2 terms in the following sequence? -3, 0, 3, 6, 9,… A. 11, 13 B. 11, 15 C. 12, 15 D. 10, 11 11. Find the sum of the following infinite geometric series, if it exists. 2 + 1.5 + 1.125 + 0.8437 +… A. Does not exist B. 8 C. 10 D. 12 12. The following is a geometric sequence. 1, 5, -25, 125, … A. true B. false
PLEASE HELP! ALGEBRA II Sequences and series?
I need so much help on this and I know its not multiple choice, but please, please, please help... Or even if you know of a solver or something to help me... I really haven't been able to find a good solver, or a solver for each question, but I prefer if you do help me out with the answer... Thank you :) 1.Find the three arithmetic means between 10 and 18. 10,___,___,___,18 2.Find the three arithmetic means between 7 and 21. 7,___,___,___,21 3.Find the sixth term of an arithmetic sequence with t1 = 2 and tn = tn-1 + 4. 4.Find S10 for the series 2 + 7 + 12 + 17 +... 5.Find S15 for the series -1 + -3 + -5 + -7 +... 6.Find S20 for the series -1 + -3 + -5 + -7 +... 7.Find the four geometric means between 4 and 972 4,___,___,___,___,972 8.Find the 6th term of the sequence in which t1 = -5 and tn = -5tn-1. 9.Find S8 for the series -2+-10+-50+-250... 10.Find S10 for the series 1 + 1.5 + 2.25 + 3.375 +... 11.Find S9 for the series 1 + 5 + 25 + 125 +... 12.Find S10 for the series 1 + 2 + 4 + 8 +... 13.Find the sum of the infinite series if it exists. If it exists, round to one decimal place. If it does not exist, type none. 1/3+4/9+16/27+64/81+... 14.Find the sum of the infinite series if it exists. If it exists, round to one decimal place. If it does not exist, type none. 3 + 1.2 + 0.48 + 0.192 + ... 15.Find the sum of the infinite series if it exists. If it exists, round to one decimal place. If it does not exist, type none. 4 + 3.2 + 2.56 + 2.048 +... 16.Find the sum of the infinite series if it exists. If it exists, round to one decimal place. If it does not exist, type none. 8 + 4 + 2 + 1 +... This makes absolutely no sense to me, after spending hours and hours on it :P Thanks in advance for answering!
Is there a algebraic expression for the sequence 2,4,8,10?
Assuming we’re representing numbers in standard decimal…For any list of N numbers, there is a unique N-1 degree polynomial that gives these values for x=1, 2, 3, 4… (This fact is behind a multiplication technique called the Schönhage–Strassen algorithm)After getting bored with so many “what is the next number in this sequence” questions on Quora (some of them, admittedly random!) I wrote a computer program to find these polynomial and reply to the question automatically. This had two unintended consequences: first, it resulted in more sequence problems being recommended to me, and second it resulted in a temporary suspension for writing many similar responses.It’s probably not what you’re looking for, but here it is anyway, in case it helps.This is a generated answer.The degree-3 polynomial that produces these numbers for x=1, 2, 3, ... is:[math]-\frac{2}{3}x^3+5x^2-\frac{25}{3}x+6[/math]The next item in the sequence is 6.