answer the following

Question

For the given arithmetic sequence,

(a) Identify the common difference, d.

(b) Write a recursive formula.

(c) Write a non-recursive formula for the nth term, a_n

(d) Find the 20th and 50th terms.

1. 5, -1, -7, -13, -19, ...
2. 3/2, 4, 13/2, 9, 23/2 ...

Answer 1

common difference, d = -6. each term is 6 less than the preceding term

d = AN - A(N-1) = difference in two consecutive terms of the sequence: A2-A1 = -1-5 = -6

A1 =5

A2 =5+d = -1

A3 =5+2d =-7

AN =A1 +(N-1)d

AN = 5-(N-1)(6)= 5-6N+6 = 11-6N

AN =11-6N

A1 = 11-6(1) = 5

A2 = 11-6(2) = -1

A3 = 11-6(3) = -7

A20 = 11-6(20) = 11-120= -109

A50 = 11-6(50) = 11-300 = -289

common difference = 5/2

A1 = 3/2

A2 = 3/2 +5/2 = 8/2 = 4

AN = A1 +(N-1)d

AN=3/2 +(N-1)(5/2) = 3/2 + (5/2)N - 5/2 = (5/2)N -1

AN =5N/2 -1

A20 = 5(20)/2 -1 = 49

A50 = 5(50)/2= 124

A