Determine the number of terms in the sequence
-5;-1;3;7;....;35
d=4
(35 - (-5))/4 + 1 = ___
or, -5+4(n-1) = 35
To determine the number of terms in the given arithmetic sequence, we need to figure out the common difference between the terms and the last term.
The common difference (d) can be found by subtracting the second term from the first term (d = -1 - (-5) = 4).
The last term (L) of the sequence can be found using the formula:
L = first term + (number of terms - 1) * common difference
Here, the first term (A) is -5, and the last term (L) is 35.
35 = -5 + (number of terms - 1) * 4
40 = (number of terms - 1) * 4 [subtracting -5 from both sides]
10 = number of terms - 1 [dividing both sides by 4]
11 = number of terms
Therefore, there are 11 terms in the given sequence.
To determine the number of terms in a sequence, we need to find the difference between the first and last terms, and then divide it by the common difference.
In this sequence, the first term is -5, and the last term is 35. The common difference between consecutive terms is the same, which is 4 in this case.
To find the difference between the first and last terms, we subtract the first term from the last term: 35 - (-5) = 40.
Now, we divide this difference by the common difference: 40 / 4 = 10.
Therefore, the number of terms in the sequence is 10.