Write the first five terms of the sequence in which the nth term is a_n = (n+1) !/n+1.

a) 1,2,6,24,120

b) 1,2,3,4,5

c) 1,1,3,12,60

d) 1,1,1,1,1

Answer:a) 1,2,6,24,120

Step-by-step explanation:

The formula for the nth term of the sequence is expressed as

n = (n+1) !/n+1

For the first term, n = 1. Therefore,

(1+1) ! / (1+1) = 2!/2 = (2*1) / 2 = 1

For the second tern, n = 2. Therefore,

(2+1) !/2+1 = 3! / 3 = (3*2*1) / 3 = 6/3 = 2

For the third term, n = 3, therefore

(3+1) !/3+1 = 4!/4 = (4*3*2*1) / 4 = 6

For the fourth term, n = 4. Therefore

(4+1) !/4+1 = 5!/5 = (5*4*3*2*1) / 5 = 24

For the fifth term, n = 5. Therefore

(5+1) !/5+1 = 6!/6 = 6 * 5*4*3*2*1) / 6 = 120

Answer: a) 1,2,6,24,120