Find the 100th term in the sequence 77, 71, 65, 59
How do you go about doing this question without the need to list them all out?
note that each term is 6 less than the previous one.
So, the 100th term is 6*99 less than the 1st term.
. . .
thanks!
To find the 100th term in the sequence without listing them all out, we need to identify the pattern and use it to calculate the desired term.
In this sequence, we can observe that each term is obtained by subtracting 6 from the previous term.
To find the 100th term, we need to write down the general formula for the nth term of the sequence. We can denote the first term as a (which is 77 in this case) and the common difference as d (which is -6).
The formula to calculate the nth term in an arithmetic sequence is:
nth term = a + (n-1)d
Plugging in the values for this specific sequence:
nth term = 77 + (100-1)(-6)
Simplifying the equation:
nth term = 77 - 594
Calculating:
nth term = -517
Therefore, the 100th term in the sequence 77, 71, 65, 59 is -517.
To find the 100th term in the sequence without listing out each individual term, we need to recognize the pattern in the sequence.
Looking at the given sequence 77, 71, 65, 59, we can observe that the terms are decreasing by 6 each time.
To find the nth term in the sequence, we can use the formula:
nth term = first term + (n - 1) * common difference
Here, the first term is 77 and the common difference is -6 (as the terms are decreasing).
Plugging the values into the formula, we get:
100th term = 77 + (100 - 1) * (-6)
Simplifying this, we have:
100th term = 77 + 99 * (-6)
= 77 - 594
= -517
Therefore, the 100th term in the sequence 77, 71, 65, 59 is -517.