Find the first four terms of the sequence given by the follo

Find the first four terms of the sequence given by the following. a_n = 3^n/2n + 1, n = 1, 2, 3, ...

Solution

a_n= 3ⁿ/(2ⁿ+1)

n=1 a₁=3¹/(2¹+1)=3/3=1

n=2

a₂=3²/(2²+1) = 9/5

n=3

a₃=3³/(2³+1)= 27/9= 3

n=4

a₄=3⁴/(2⁴+1) = 81/17

Hence the four terms are

1, 9/5, 3, 81/17