What is the 2011th term of the arithmetic sequence -4,-1,2,5...., where each term after the first is 3 more than the preceding term? (Remeber -4 is the first term of the sequence)
To find the 2011th term of the arithmetic sequence, we can start by observing the pattern of the sequence. The sequence starts with -4 and each term after the first is 3 more than the preceding term.
We can determine the nth term of an arithmetic sequence using the formula:
nth term = first term + (n - 1) * common difference
In this case, the first term is -4 and the common difference is 3.
Let's substitute these values into the formula to find the desired term:
2011th term = -4 + (2011 - 1) * 3
Simplifying the expression within the parentheses:
2011th term = -4 + 2010 * 3
Multiplying:
2011th term = -4 + 6030
Calculating the sum:
2011th term = 6026
Therefore, the 2011th term of the sequence is 6026.