Find the sum of the following arithmetic series:
3plus9plus15plus21plus...plus81.
In this series, the first term (a) is 3, the common difference (d) is 6, and the last term (l) is 81.
To find the number of terms in the series, we use the formula for the nth term of an arithmetic series:
l = a + (n-1)d
81 = 3 + (n-1)6
78 = 6(n-1)
78 = 6n - 6
84 = 6n
n = 14
Now that we have the number of terms, we can find the sum of the series using the formula:
S = n/2 * (a + l)
S = 14/2 * (3 + 81)
S = 7 * 84
S = 588
Therefore, the sum of the arithmetic series 3 + 9 + 15 + 21 + ... + 81 is 588.