What is the value of the 30th term in the following arithmetic sequence?
12, 6, 0, -6, ...
a = 12
d = -6
T30 = a+29d
so, . . .
To find the value of the 30th term in an arithmetic sequence, you need to know the common difference, denoted as d, and the first term, denoted as a₁.
Given the arithmetic sequence: 12, 6, 0, -6, ...
We can observe that the common difference d is -6 subtracted from 0, which gives us -6 - 0 = -6.
The first term a₁ is given as 12.
Now we can use the formula to find the nth term of an arithmetic sequence:
aₙ = a₁ + (n-1)d
Substituting the values into the formula:
a₃₀ = 12 + (30-1)(-6)
Simplifying:
a₃₀ = 12 + 29(-6)
Continuing to simplify:
a₃₀ = 12 - 174
Finally, calculating:
a₃₀ = -162
Therefore, the value of the 30th term in the arithmetic sequence is -162.
To find the value of the 30th term in an arithmetic sequence, we need to determine the pattern and then apply the formula for the nth term.
In this sequence, each term is obtained by subtracting 6 from the previous term. So, the common difference is -6.
The formula to find the nth term in an arithmetic sequence is given by:
an = a1 + (n - 1)d
Where:
an is the nth term,
a1 is the first term,
n is the position of the term,
d is the common difference.
In the given sequence:
a1 = 12 (the first term)
d = -6 (the common difference)
Now, substitute these values into the formula:
a30 = 12 + (30 - 1)(-6)
Simplify the equation:
a30 = 12 + 29(-6)
a30 = 12 - 174
a30 = -162
Therefore, the value of the 30th term in the given sequence is -162.