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?( remember -4 is the first term of the sequence.)
-4 + (3 * 2110)
To find the 2011th term of an arithmetic sequence, we need to determine the general formula for the sequence, and then plug in the value of n to find the desired term.
In this case, we are given that the first term of the sequence is -4, and each subsequent term is 3 more than the previous term. We can find the general formula for an arithmetic sequence using the formula:
an = a1 + (n - 1)d,
where an represents the nth term of the sequence, a1 is the first term, n is the position of the term, and d is the common difference between consecutive terms. In this sequence, the first term a1 is -4.
To find the common difference d, we observe that each term is 3 more than the previous term. Therefore, the common difference is 3.
Now we can substitute the values into the formula:
a2011 = -4 + (2011 - 1)3.
Simplifying this expression:
a2011 = -4 + 2010 * 3.
a2011 = -4 + 6030.
a2011 = 6026.
Therefore, the 2011th term of the given sequence is 6026.