Question

Write the 1st 5 terms of each sequence, whose nth term is
an =[ (-1)^n (2n+1) ] / 6

Answer 1

Just by putting the values for n , you can get the terms.
now, n=1
a1 = {(-1)^1 (2*1+1)}/6
a1 = -1(3)/6 = -1/2.

n= 2
a2 = {(-1)^2(2*2+1)}/6
a2= 1*5/6 = 5/6

n=3
a3 = {(-1)^3(2*3+1)}/6
a3 = {-1*7}/6 = -7/6

n=4
a4 = {-1^4(2*4+1)}/6
a4 = 9/6 = 3/2.

n= 5
a5 = {-1^5(2*5+1)}/6
a5 = -1*11/6 = -11/6

So, the terms are -1/2,5/6,-7/6,3/2,-11/6.

Answer 2

first 5 terms are putting n=1,2,3,4,5
so the terms are
(-1/2), (5/6), (-7/6), (9/6), (-11/6)