To find the sum of the finite arithmetic sequence defined by the expression 4n + 10 for n ranging from 1 to 18, we can follow these steps:
- Determine the terms in the sequence: We need to calculate the values of the expression for each integer value of n from 1 to 18.
- Calculate the terms: Computing the first few terms:
- For n = 1: 4(1) + 10 = 14
- For n = 2: 4(2) + 10 = 18
- For n = 3: 4(3) + 10 = 22
- For n = 4: 4(4) + 10 = 26
- … (continue this till n = 18)
- For n = 18: 4(18) + 10 = 82
Now, we can see that the first term (when n=1) is 14 and the last term (when n=18) is 82. The sequence is:
- 14, 18, 22, 26, …, 82
- Use the formula for the sum of an arithmetic sequence: The sum S of an arithmetic sequence can be found using the formula:
S = (number of terms / 2) * (first term + last term)
- Calculate the total number of terms: From n=1 to n=18, we have:
Number of terms = 18
- Now plug in the values into the sum formula:
S = (18 / 2) * (14 + 82) = 9 * 96 = 864
Therefore, the sum of the finite arithmetic sequence from n=1 to n=18 using the expression 4n + 10 is 864.