the first term of the arithmetic sequence is -37 and the second term is-30 what is the smallest positive term of the sequence?
Well, well, well, looks like we've got ourselves an arithmetic sequence here. Now, the common difference between consecutive terms is given by the second term minus the first term. So, in this case, we have -30 - (-37), which simplifies to 7.
To find the smallest positive term, we need to find the smallest positive integer multiple of 7. Drumroll, please... And the winner is 7 itself! So, the smallest positive term of the sequence is 7. Congrats to the lucky number 7!
To find the common difference of the arithmetic sequence, we can subtract the first term from the second term.
Common difference = -30 - (-37)
Common difference = -30 + 37
Common difference = 7
Now, to find the smallest positive term of the sequence, we need to determine the number of steps needed to reach a positive term from the first term.
Since the common difference is positive (7), the sequence is increasing. We can start from the first term (-37) and keep adding the common difference (7) until we reach a positive term.
First term: -37
Second term: -37 + 7 = -30
Third term: -30 + 7 = -23
Fourth term: -23 + 7 = -16
Fifth term: -16 + 7 = -9
Sixth term: -9 + 7 = -2
Seventh term: -2 + 7 = 5
Therefore, the smallest positive term in the sequence is 5.
To find the smallest positive term of an arithmetic sequence, we need to determine the common difference first.
In an arithmetic sequence, the common difference is the difference between any two consecutive terms.
Given that the first term is -37 and the second term is -30, we can find the common difference by subtracting the first term from the second term:
Common difference = second term - first term
= (-30) - (-37)
= -30 + 37
= 7
Now that we know the common difference is 7, we can find the nth term of the arithmetic sequence using the formula:
nth term = first term + (n - 1) * common difference
To find the smallest positive term, we start with n = 1 and keep increasing n until we get a positive term.
Let's start calculating the terms:
n = 1: nth term = -37 + (1 - 1) * 7 = -37
n = 2: nth term = -37 + (2 - 1) * 7 = -30
n = 3: nth term = -37 + (3 - 1) * 7 = -23
n = 4: nth term = -37 + (4 - 1) * 7 = -16
n = 5: nth term = -37 + (5 - 1) * 7 = -9
n = 6: nth term = -37 + (6 - 1) * 7 = -2
n = 7: nth term = -37 + (7 - 1) * 7 = 5
As we can see, the smallest positive term is 5.
Therefore, the smallest positive term of the arithmetic sequence is 5.