Given information:
- Sum of n terms of an Arithmetic Progression (AP) = 136
- Common difference (d) = 4
- Last term (a_n) = 31

To find:
The number of terms in the AP.

Solution:
Step 1: Finding the first term (a_1)
We know that the formula to find the sum of n terms of an AP is given by:

Sum (S_n) = (n/2) * (2a_1 + (n-1)d)

Substituting the given values, we have:
136 = (n/2) * (2a_1 + (n-1) * 4)

Simplifying the equation, we get:
136 = (n/2) * (2a_1 + 4n - 4)

We also know that the last term (a_n) is given by:
a_n = a_1 + (n-1)d

Substituting the given values, we have:
31 = a_1 + (n-1) * 4

Step 2: Solving the equations
We have two equations with two unknowns (a_1 and n). We can solve these equations simultaneously to find the values.

Let's solve the second equation for a_1:
a_1 = 31 - 4(n-1)
a_1 = 31 - 4n + 4

a_1 = -4n + 35

Substituting this value of a_1 in the first equation, we have:
136 = (n/2) * (2(-4n + 35) + 4n - 4)

Simplifying the equation, we get:
136 = (n/2) * (-8n + 70 + 4n - 4)

136 = (n/2) * (-4n + 66)

Multiplying both sides by 2 to eliminate the denominator, we have:
272 = -4n^2 + 66n

Rearranging the equation, we get:
4n^2 - 66n + 272 = 0

Step 3: Solving the quadratic equation
We can solve the quadratic equation using factoring, completing the square, or the quadratic formula. In this case, let's use the quadratic formula:

n = (-b ± √(b^2 - 4ac)) / (2a)

Substituting the values, we have:
n = (-(-66) ± √((-66)^2 - 4(4)(272))) / (2(4))

Simplifying the equation, we get:
n = (66 ± √(4356 - 4352)) / 8
n = (66 ± √4) / 8

n = (66 ± 2) / 8

Now, we have two possible values for n:
n = (66 + 2) / 8 = 68 / 8 = 8.5
n = (66 - 2) / 8 = 64 / 8 = 8

However, the number of terms cannot be a decimal. Therefore, the number of terms is 8.