Question 557365
2. a_n = (n + 1)^3
first 6 terms: 2^3, 3^3, 4^3, 5^3, 6^3, 7^3 ----> 8, 27, 64, 125, 216, 343


4. a_n = n/(n+3)
first 6 terms: 1/4, 2/5, 1/2, 4/7, 5/8, 2/3


6. -3, 6, -12, 24 ---> next term = 24(-2) = -48
formula: a_n = (-3)(-2)^(n-1)


8. 4 + 8 + 12 + 16 = sum n from 1 to 4, 4n


10. 0 + 3 + 6 + 9 + 12 = sum n from 0 to 4, 3n


12. n from 4 to 10, n(2n-1)
sum = (4)(7) + (5)(9) + (6)(11) + (7)(13) + (8)(15) + (9)(17) + (10)(19) = 693


14. k from 1 to 30, 4
sum = 4(30) = 120


16. 4, 6, 8, 10, 12
a_n = 4 + 2(n - 1) = 2n + 2


18. d = 5, a_1 = 13 ----> a_n = 13 + 5(n-1) = 5n + 8


20. a_4 = 20, a_(13) = 65 (use system of equations)
a + 3d = 20
a + 12d = 65
Use any method (graphing, elimination, substitution) to solve and get a = 5, d = 5

equation: a_n = 5 + 5(n-1) = 5n


26. 6, 12, 24, 48
rule: a_n = (6)(2)^(n-1)


28. a_1 = 6, r = 3 ----> a_n = (6)(3)^(n-1)


30. a_2 = 50, a_6 = 0.005
ar = 50
ar^5 = 0.005 ----> a = 500, r = 1/10
formula: a_n = (500)(1/10)^(n-1)