Find the sum of the first 20 terms of the series 8, 12, 16, ....., 96
Answer Details
To find the sum of the first 20 terms of the series 8, 12, 16, ....., 96, we need to find the common difference between the terms first. We can do this by subtracting any two consecutive terms, such as:
12 - 8 = 4
16 - 12 = 4
...
96 - 92 = 4
So, the common difference between the terms is 4.
Next, we can use the formula for the sum of an arithmetic series to find the sum of the first 20 terms:
S = (n/2)(a1 + an)
Where S is the sum of the series, n is the number of terms, a1 is the first term, and an is the nth term.
Using this formula, we have:
S = (20/2)(8 + 96)
S = 10(104)
S = 1040
Therefore, the sum of the first 20 terms of the series 8, 12, 16, ....., 96 is 1040.