Find the sum of the first 30 terms of the arithmetic sequence 10,5,0,-5
To find the sum of the first 30 terms of an arithmetic sequence, we can use the formula:
\[ S_n = \frac{n}{2}[2a + (n-1)d] \]
where:
\( S_n \) is the sum of the first \( n \) terms,
\( a \) is the first term,
\( d \) is the common difference between the terms, and
\( n \) is the number of terms.
In this case, the first term (\( a \)) is 10, the common difference (\( d \)) is -5, and the number of terms (\( n \)) is 30.
Plugging these values into the formula:
\[ S_{30} = \frac{30}{2}[2(10) + (30-1)(-5)] \]
\[ S_{30} = 15[20 + 29(-5)] \]
\[ S_{30} = 15[20 - 145] \]
\[ S_{30} = 15(-125) \]
\[ S_{30} = -1875 \]
Therefore, the sum of the first 30 terms of the arithmetic sequence 10, 5, 0, -5 is -1875.