An arithmetic sequence begins, 116, 109, 102
Find the 300th term of this sequence.
Thank you!
a = 116
d = -7
n = 300
term(n) = a + (n-1)d
= 116 + 299(-7) = -1977
To find the 300th term of an arithmetic sequence, we need to find the common difference first.
Given the first three terms of the sequence: 116, 109, 102, we can find the common difference (d) by subtracting the second term from the first term, and then subtracting the third term from the second term.
Common difference (d) = 109 - 116 = -7
Common difference (d) = 102 - 109 = -7
Since the common difference is the same in this sequence, we can conclude that the common difference (d) is -7.
Now, we can use the formula to find the nth term of an arithmetic sequence:
nth term (Tn) = first term (a) + (n - 1) * common difference (d)
Substituting the values into the formula:
T300 = 116 + (300 - 1) * (-7)
T300 = 116 + 299 * (-7)
Now we can calculate the 300th term:
T300 = 116 + (-2093)
T300 = -1977
Therefore, the 300th term of this arithmetic sequence is -1977.
To find the 300th term of an arithmetic sequence, we need to first find the common difference (d), which is the difference between adjacent terms.
In this case, we can see that the difference between the first and second terms is -7 (116 - 109), and the difference between the second and third terms is also -7 (109 - 102). Since the common difference remains constant, we conclude that d = -7.
To find the nth term of an arithmetic sequence, we use the formula:
term_n = a + (n - 1) * d
where:
term_n is the nth term of the sequence,
a is the first term of the sequence,
n is the position of the term in the sequence, and
d is the common difference.
Now, let's substitute the values we know into the formula:
a = 116 (first term)
n = 300 (position of the term)
d = -7 (common difference)
term_300 = 116 + (300 - 1) * -7
= 116 + 299 * -7
= 116 - 2093
= -1977
Therefore, the 300th term of this arithmetic sequence is -1977.