Find the 100th term in the sequence 77,71,65,59,....
The fact that you need to find the 100th term means you need to find the general rule of T(n), the nth term.
Since the difference between terms is 71-77=-6, we conclude that
T(n)=-6n+k
We know that the first term, T(1) = 77.
Therefore 77=-6(1)+k, or k=83
Thus the general rule is
T(n) = 83-6n
I'll leave it to you to find the 100th term.
-517
To find the 100th term in the given sequence, we can first determine the pattern of the sequence.
We can observe that each term in the sequence is decreasing by 6 from the previous term.
Starting with the first term, 77:
77 - 6 = 71
71 - 6 = 65
65 - 6 = 59
...
Therefore, the common difference between consecutive terms is -6.
We can now use the formula for the nth term of an arithmetic sequence to find the 100th term.
The formula for the nth term of an arithmetic sequence is:
nth term = first term + (n-1) * common difference
In this case:
first term = 77
common difference = -6
n = 100
Plugging these values into the formula:
100th term = 77 + (100 - 1) * -6
= 77 + 99 * -6
= 77 - 594
= -517
Therefore, the 100th term in the sequence 77, 71, 65, 59, ... is -517.
To find the 100th term in the given sequence 77, 71, 65, 59, ..., we need to first observe the pattern or the relationship between the terms.
From the given sequence, we can see that each term is decreasing by 6. Therefore, we can write the sequence as:
77, 77 - 6, 77 - 2 * 6, 77 - 3 * 6, ...
We can generalize the nth term of this sequence as:
nth term = 77 - (n - 1) * 6
Now, we can substitute n = 100 into the formula to find the 100th term:
100th term = 77 - (100 - 1) * 6
= 77 - 99 * 6
= 77 - 594
= -517
Therefore, the 100th term in the sequence 77, 71, 65, 59, ... is -517.