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.)
(I posted this before but it was the wrong answer)
To find the 2011th term of an arithmetic sequence, we can use the formula for the nth term of an arithmetic sequence:
tn = a + (n - 1) * d
Where:
tn is the nth term
a is the first term
n is the term number
d is the common difference
In this case, the first term a is -4, and the common difference d is 3.
Substituting the values into the formula, we have:
t2011 = -4 + (2011 - 1) * 3
= -4 + 2010 * 3
= -4 + 6030
= 6026
Therefore, the 2011th term of the arithmetic sequence is 6026.
To find the 2011th term of the arithmetic sequence −4, −1, 2, 5, ..., where each term after the first is 3 more than the preceding term, we need to determine the pattern and then apply it.
In this arithmetic sequence, each term (except the first) is obtained by adding 3 to the previous term. So, the common difference (d) of the sequence is 3.
To find the nth term (Tn) of an arithmetic sequence, we can use the following formula:
Tn = a + (n - 1)d
Where:
a = first term
n = position of the term we want to find
d = common difference
In this case, the first term (a) is -4 and the common difference (d) is 3. We want to find the 2011th term, so n = 2011.
Using the formula, we can substitute the given values:
T2011 = -4 + (2011 - 1)3
Simplifying the equation:
T2011 = -4 + 2010 * 3
T2011 = -4 + 6030
T2011 = 6026
Therefore, the 2011th term of the arithmetic sequence is 6026.
I answered this before
you start with -4
then add 3 , 2010 times
-4 + 6030 is the 2011th term
-4,-1,2,5 there all adding 3
You want to subtract 3 to -4 to find the 0th term
-4-3= -7
So the equation is y=-7+3x
Sub in 2011 for x
y=-7+3*2011
y=6026