Calculating the number of terms in an arithmetic progression might seem like a complex operation, but in reality it is a simple and straightforward process. All that needs to be done is to insert the known values of the progression into the formula t = a + (n - 1) d, and solve the equation based on n, which represents the number of terms in the sequence. Note that the variable t of the formula represents the last number of the sequence, the parameter a is the first term of the progression and the parameter d represents the reason, that is the constant difference existing between each term of the numerical sequence and the previous one.
Steps
Step 1. Identify the first, second and last numbers of the arithmetic progression under consideration
Normally, in the case of mathematical problems such as the one in question, the first three (or more) terms of the sequence and the last are always known.
For example, assume that you need to examine the following progression: 107, 101, 95… -61. In this case, the first number in the sequence is 107, the second is 101, and the last is -61. To solve the problem you need to use all this information
Step 2. Subtract the first term in the sequence from the second to calculate the reason for the progression
In the proposed example the first number is 107, while the second is 101, so doing the calculations you will get 107 - 101 = -6. At this point you know that the reason for the arithmetic progression under consideration is equal to -6.
Step 3. Use the formula t = a + (n - 1) d and solve the calculations based on n.
Replace the parameters of the equation with the known values: t with the last number of the sequence, a with the first term of the progression and d with the reason. Perform the calculations to solve the equation based on n.
