Answer
Here are the first 10 terms of each sequence:
*Sequence a) Starting with 10, subtracting 3*
1. 10
2. 7
3. 4
4. 1
5. -2
6. -5
7. -8
8. -11
9. -14
10. -17
*Sequence b) Sum of first n positive integers*
1. 1
2. 3 (1+2)
3. 6 (1+2+3)
4. 10 (1+2+3+4)
5. 15 (1+2+3+4+5)
6. 21 (1+2+3+4+5+6)
7. 28 (1+2+3+4+5+6+7)
8. 36 (1+2+3+4+5+6+7+8)
9. 45 (1+2+3+4+5+6+7+8+9)
10. 55 (1+2+3+4+5+6+7+8+9+10)
*Sequence c) 3^n - 2^n*
1. 3^1 - 2^1 = 1
2. 3^2 - 2^2 = 5
3. 3^3 - 2^3 = 19
4. 3^4 - 2^4 = 65
5. 3^5 - 2^5 = 211
6. 3^6 - 2^6 = 665
7. 3^7 - 2^7 = 2059
8. 3^8 - 2^8 = 6305
9. 3^9 - 2^9 = 19279
10. 3^10 - 2^10 = 59049
*Sequence d) Floor of sqrt(n)*
1. floor(sqrt(1)) = 1
2. floor(sqrt(2)) = 1
3. floor(sqrt(3)) = 1
4. floor(sqrt(4)) = 2
5. floor(sqrt(5)) = 2
6. floor(sqrt(6)) = 2
7. floor(sqrt(7)) = 2
8. floor(sqrt(8)) = 2
9. floor(sqrt(9)) = 3
10. floor(sqrt(10)) = 3
*Sequence e) Fibonacci-like*
1. 1
2. 5
3. 6 (1+5)
4. 11 (5+6)
5. 17 (6+11)
6. 28 (11+17)
7. 45 (17+28)
8. 73 (28+45)
9. 118 (45+73)
10. 191 (73+118)
*Sequence f) Largest integer with n bits*
1. 1 (2^0)
2. 3 (2^1+2^0)
3. 7 (2^2+2^1+2^0)
4. 15 (2^3+2^2+2^1+2^0)
5. 31 (2^4+2^3+2^2+2^1+2^0)
6. 63 (2^5+2^4+2^3+2^2+2^1+2^0)
7. 127 (2^6+2^5+2^4+2^3+2^2+2^1+2^0)
8. 255 (2^7+2^6+2^5+2^4+2^3+2^2+2^1+2^0)
9. 511 (2^8+2^7+2^6+2^5+2^4+2^3+2^2+2^1+2^0)
10. 1023 (2^9+2^8+2^7+2^6+2^5+2^4+2^3+2^2+2^1+2^0)
Please let me know if you have any questions or if you'd like more terms!
Work Step by Step
Here are the first 10 terms of each sequence:
*Sequence a) Starting with 10, subtracting 3*
1. 10
2. 7
3. 4
4. 1
5. -2
6. -5
7. -8
8. -11
9. -14
10. -17
*Sequence b) Sum of first n positive integers*
1. 1
2. 3 (1+2)
3. 6 (1+2+3)
4. 10 (1+2+3+4)
5. 15 (1+2+3+4+5)
6. 21 (1+2+3+4+5+6)
7. 28 (1+2+3+4+5+6+7)
8. 36 (1+2+3+4+5+6+7+8)
9. 45 (1+2+3+4+5+6+7+8+9)
10. 55 (1+2+3+4+5+6+7+8+9+10)
*Sequence c) 3^n - 2^n*
1. 3^1 - 2^1 = 1
2. 3^2 - 2^2 = 5
3. 3^3 - 2^3 = 19
4. 3^4 - 2^4 = 65
5. 3^5 - 2^5 = 211
6. 3^6 - 2^6 = 665
7. 3^7 - 2^7 = 2059
8. 3^8 - 2^8 = 6305
9. 3^9 - 2^9 = 19279
10. 3^10 - 2^10 = 59049
*Sequence d) Floor of sqrt(n)*
1. floor(sqrt(1)) = 1
2. floor(sqrt(2)) = 1
3. floor(sqrt(3)) = 1
4. floor(sqrt(4)) = 2
5. floor(sqrt(5)) = 2
6. floor(sqrt(6)) = 2
7. floor(sqrt(7)) = 2
8. floor(sqrt(8)) = 2
9. floor(sqrt(9)) = 3
10. floor(sqrt(10)) = 3
*Sequence e) Fibonacci-like*
1. 1
2. 5
3. 6 (1+5)
4. 11 (5+6)
5. 17 (6+11)
6. 28 (11+17)
7. 45 (17+28)
8. 73 (28+45)
9. 118 (45+73)
10. 191 (73+118)
*Sequence f) Largest integer with n bits*
1. 1 (2^0)
2. 3 (2^1+2^0)
3. 7 (2^2+2^1+2^0)
4. 15 (2^3+2^2+2^1+2^0)
5. 31 (2^4+2^3+2^2+2^1+2^0)
6. 63 (2^5+2^4+2^3+2^2+2^1+2^0)
7. 127 (2^6+2^5+2^4+2^3+2^2+2^1+2^0)
8. 255 (2^7+2^6+2^5+2^4+2^3+2^2+2^1+2^0)
9. 511 (2^8+2^7+2^6+2^5+2^4+2^3+2^2+2^1+2^0)
10. 1023 (2^9+2^8+2^7+2^6+2^5+2^4+2^3+2^2+2^1+2^0)
Please let me know if you have any questions or if you'd like more terms!
