For the rule of 78, for a 12-month period, the last term in the sequence is 12 and the series sums to 78. for an 14 month period, the last term is and the series sum is . for a 16 month period, the last term is and the series sum is . for a 20 month period, the last term is and the series sum is.

We can solve this question using the formula below-

The formula for sum of n terms is,

For 14 months the last term is 14 and its sum is,

Here a = 1 and d = 1

For 16 months the last term is 16 and its sum is,

Here a = 1 and d = 1

OR

We can also solve this using simple addition like-

1. For a 14 month period the last term in the sequence is 14 and the series sum is;

2. For a 16 month period, the last term is 16 and the series sum is;

3. For a 16 month period, the last term is 20 and the series sum is;

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

eventually after a few more steps, your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x