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)
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
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.