Consider the arithmetic sequence 25811 a Find u101 b Find th

Consider the arithmetic sequence 2,5,8,11... (a) Find u101 (b) Find the value of n so that un=152

Solution

2,5,8,11,.........

first term u₀ is 2

common difference d=3

nth term of arithmetic sequence is given by

u_n=u₁+(n-1)d

u₁₀₁=(2) + (101-1)3 = 302

u_n=152

152= 2+(n-1)3

152= 3n-1

3n=153

n=51