Sum of First n Terms of an AP The sum of the first n terms of an arithmetic progression (AP) can be calculated using the formula: Sum = n/2 (a + an-1)...
Sum of First n Terms of an AP
The sum of the first n terms of an arithmetic progression (AP) can be calculated using the formula:
Sum = n/2 * (a + an-1)
where:
Sum is the sum of the first n terms.
n is the number of terms in the AP.
a is the first term in the AP.
an is the last term in the AP.
Example:
Let's consider the AP with the first term a = 10 and the common difference d = 2. The last term in the AP would be an = 22. Using the formula, we can calculate the sum as:
Sum = n/2 * (a + an-1) = 5 * (10 + 22) = 110
Interpretation:
The sum of the first n terms of an AP represents the sum of the values of each term in the sequence. It can be interpreted as the total "area" of the arithmetic progression, where each term contributes equally to the sum.
Additional Notes:
The sum of an AP can also be calculated using the formula Sum = (a + an)/2, but this formula works only if the difference between consecutive terms is constant.
The sum of an AP can be used to find the missing terms in a sequence, given the first and last terms.
The sum of an AP can also be used to find the average of a sequence of numbers