Consider the arithmetic sequence 2, 5, 8, 11, ... a) Find U101 b) Find the value of n so that Un = 152

Firstly, as with any question, make sure to check your formula book in order to find any relevant equations. In this case, the one most relevant to us is U_n = U₁ + d(n-1).
From here we will need to find the common difference of the sequence, 'd'. You could do this by substituting the information we have into the formula, but a much simpler way would be to take the first term of the sequence away from the second; so 5 - 2 = 3. We can check this by taking the second away from the third, 8 - 5 = 3. Therefore, d = 3.
a) We can now substitute our information into the equation to find U_101, 
U₁₀₁ = U₁ + d(n-1)
We know that n = 101, U₁ is the first term of the sequence, 2, and that d = 3.
So, U₁₀₁ = 2 + 3(101-1)
Solving this gets us to U₁₀₁ = 2 + 3(100), U₁₀₁ = 2 + 300, U₁₀₁ = 302.

b) Here we start by again substituting our given information into the formula.
152 = 2 + 3(n-1)
We can see that in this instance 'n' is the unknown term.
By rearranging our equation we will be able to solve for n.
So, we need our common terms to be on the same side of the equation:
Minus two from both sides gives us 150 = 3(n-1).
Dividing by 3 will then give us 50 = n - 1
Now we just need to add 1 to both sides leaving us with 51 = n.