sequence | MathCelebrity Forum

# sequence

1. ### A new company is projecting its profits over a number of weeks. They predict that their profits each

A new company is projecting its profits over a number of weeks. They predict that their profits each week can be modeled by a geometric sequence. Three weeks after they started, the company's projected profit is \$10,985.00 Four weeks after they started, the company's projected profit is...
2. ### 9, 3, 1, 1/3, 1/9 What is the next number in this sequence? What is the function machine for this se

9, 3, 1, 1/3, 1/9 What is the next number in this sequence? What is the function machine for this sequence? We see the following pattern in this sequence: 9 = 9/3^0 3 = 9/3^1 1 = 9/3^2 1/3 = 9/3^3 1/9 = 9/3^4 Our function machine formula is: f(n) = 9/3^(n - 1) Next term is the 6th term: f(6)...
3. ### 3, 6, 12, 24, 48 What is the function machine for this sequence?

3, 6, 12, 24, 48 What is the function machine for this sequence? We see the following pattern: 3 * 2^0 = 3 3 * 2^1 = 6 3 * 2^2 = 12 3 * 2^3 = 24 3 * 2^4 = 48 Our function machine for term n is: f(n) = 3 * 2^(n - 1)
4. ### 1, 1/2, 1/4, 1/8, 1/16 The next number in the sequence is 1/32. What is the function machine you wou

1, 1/2, 1/4, 1/8, 1/16 The next number in the sequence is 1/32. What is the function machine you would use to find the nth term of this sequence? Hint: look at the denominators We notice that 1/2^0 = 1/1 = 1 1/2^1 = 1/2 1/2^2 = 1/4 1/2^3 = 1/8 1/2^4 = 1/32 So we write our explicit formula for...
5. ### 1/2, 3, 5&1/2, 8......203 What term is the number 203?

1/2, 3, 5&1/2, 8......203 What term is the number 203? We see the following pattern: 1/2 = 2.5*1 - 2 3 = 2.5*2 - 2 5&1/2 = 2.5*3 - 2 8 = 2.5*4 - 2 We build our function f(n) = 2.5n - 2 Set 2.5n - 2 = 203 Using our equation solver, we get: n = 82
6. ### 10, 1,000, 100,000, 10,000,000 What power of 10 is the 80th term?

10, 1,000, 100,000, 10,000,000 What power of 10 is the 80th term? We see the following pattern 10^1 = 10 10^3 = 1000 10^5 = 100,000 10^7 = 10,000,000 f(n) = 10^(2n - 1) We build the 80th term: f(80) = 10^(2(80) - 1) f(80) = 10^(160 - 1) f(80) = 10^159
7. ### 1, 8, 27, 64 What is the 10th term?

1, 8, 27, 64 What is the 10th term? We see the following pattern: 1^3 = 1 2^3 = 8 3^3 = 27 4^3 = 64 We build our sequence function using this pattern: f(n) = n^3 With n = 10, we have: f(10) = 10^3 f(10) = 1,000
8. ### 7, 10, 15, 22 What is the next number in the sequence? What is the 500th term?

7, 10, 15, 22 What is the next number in the sequence? What is the 500th term? We see that: 1^2 + 6 = 7 2^2 + 6 = 10 3^3 + 6 = 15 4^2 + 6 = 22 We build our function as f(n) = n^2 + 6 Next term in the sequence is f(5) f(5) = 5^2 + 6 f(5) = 25 + 6 f(5) = 31 Calculate the 500th term: f(500) =...
9. ### 1, 4, 9, 16, 25 What is the next number? What is the 50th term?

1, 4, 9, 16, 25 What is the next number? What is the 50th term? We see that 1^2 = 1, 2^2 = 4, 3^2 = 9, 4^2 = 16, 5^2 = 25 We build a formula for the nth term: f(n) = n^2 The next number means n = 6th term: f(6) = 6^2 = 36 The 50th term means n = 50: f(50) = 50^2 = 2500
10. ### 5, 14, 23, 32, 41....1895 What term is the number 1895?

5, 14, 23, 32, 41....1895 What term is the number 1895? Set up a point slope for the first 2 points: (1, 5)(2, 14) Using point slope formula, our series function is: f(n) = 9n - 4 To find what term 1895 is, we set 9n - 4 = 1895 and solve for n: 9n - 4 = 1895 Using our equation solver, we...
11. ### 100, 75, 50, 25, 0, -25 What is the next number? What is the 100th term?

100, 75, 50, 25, 0, -25 What is the next number? What is the 100th term? Using point slope, we get (1, 100)(2, 75) Our series function becomes f(n) = -25n + 125 The next term is the 7th term: f(7) = -25(7) + 125 f(7) = -175 + 125 f(7) = -50 The 100th term is found by n = 100: f(100) =...
12. ### -11, -9, -7, -5, -3 What is the next number? What is the 200th term in this sequence?

-11, -9, -7, -5, -3 What is the next number? What is the 200th term in this sequence? We see that Term 1 is -11, Term 2 is -9, so we do a point slope equation of (1,-11)(2,-9) to get the nth term of the formula f(n) = 2n - 13 The next number is the 6th term: f(6) = 2(6) - 13 f(6) = 12 - 13...
13. ### 3, 8, 13, 18, .... , 5008 What term is the number 5008?

3, 8, 13, 18, .... , 5008 What term is the number 5008? For term n, we have a pattern: f(n) = 5(n - 1) + 3 Set this equal to 5008 5(n - 1) + 3 = 5008 Using our equation solver, we get: n = 1002
14. ### 1.25, 2, 2.75, 3.5 What is the 100th term?

1.25, 2, 2.75, 3.5 What is the 100th term? The formula of nth term is: f(n) = 0.75n + 0.5 So the 100th term is: f(100) = 0.75(100) + 0.5 f(100) = 75 + 0.5 f(100) = 75.5
15. ### 2, 4, 6, 8....1000. What term is the number 1000?

2, 4, 6, 8....1000. What term is the number 1000? Formula for nth term is 2n If 2n = 1000, then dividing each side by 2, we see that: 2n/2 = 1000/2 n = 500
16. ### 1, 1/2, 1/3, 1/4, 1/5 What is the next number? What is the 89th term of the sequence?

1, 1/2, 1/3, 1/4, 1/5 What is the next number? What is the 89th term of the sequence? Formula for nth term is 1/n Next number is n = 5, so we have 1/5 With n = 89, we have 1/89
17. ### 0,7,14,21 What is the next number? What is the 1000th term?

0,7,14,21 What is the next number? What is the 1000th term? We're adding 7 to the last term, so we get a next term of: 21 + 7 = 28 For our nth term, we notice a pattern for the nth term of: 7n - 7 n = 1 --> 7(1) - 7 = 0 n = 2 --> 7(2) - 7 = 7 n = 3 --> 7(3) - 7 = 14 For n = 1000, we have...
18. ### 8,11,14,17,20 What is the next number? What is the 150th term?

8,11,14,17,20 What is the next number? What is the 150th term? We're adding by 3 to the last number in the sequence, so we have the next number as: 20 + 3 = 23 For the nth term, we have a formula of this: 3n + 5 3(1) + 5 = 8 3(2) + 5 = 11 3(3) + 5 = 14 With n = 150, we have: 3(150) + 5 = 450...
19. ### 5,10,15,20 What is the next number? What is the 100th term?

5,10,15,20 What is the next number? What is the 100th term? Increment is by 5, so next number is 20 + 5 = 25 Formula for nth number is 5 * n With n = 100, we have 5 * 100 = 500
20. ### If 5 is transformed into 11, and 12 is transformed into 25, then what does 15 become?

If 5 is transformed into 11, and 12 is transformed into 25, then what does 15 become? Taking a look at potential patterns, we see: 5 * 2 + 1 = 11 12 * 2 + 1 = 25 Using this formula, we have: 15 * 2 + 1 =31