determine whether each sequence is arithmetic. If so, identify the common difference and find the 32nd term of the sequence. 3,18,33,48
To determine if the sequence is arithmetic, we need to check if the difference between consecutive terms is constant.
18 - 3 = 15
33 - 18 = 15
48 - 33 = 15
Since the difference between each pair of consecutive terms is 15, the sequence is arithmetic. The common difference is 15.
To find the 32nd term, we can use the formula for the nth term of an arithmetic sequence:
an = a1 + (n-1)d
where
an is the nth term
a1 is the first term
d is the common difference
We are given the first term (a1 = 3), the common difference (d = 15), and we need to find the 32nd term (an = ?).
Plugging these values into the formula, we get:
a32 = 3 + (32-1)15
a32 = 3 + 465
a32 = 468
Therefore, the 32nd term of the sequence is 468.
is that correct
Yes, that is correct.
To determine whether the given sequence is arithmetic, we need to check if there is a common difference between each consecutive term.
Looking at the sequence: 3, 18, 33, 48
To find the common difference, we subtract each term from its previous term:
18 - 3 = 15
33 - 18 = 15
48 - 33 = 15
Since the difference between each consecutive term is the same (15), the sequence is indeed arithmetic.
The common difference is 15.
To find the 32nd term of the sequence, we can use the arithmetic sequence formula:
Term = First term + (n - 1) * Common difference
Plugging in the values:
First term (a) = 3
Common difference (d) = 15
Term number (n) = 32
Term = 3 + (32 - 1) * 15
Term = 3 + 31 * 15
Term = 3 + 465
Term = 468
Therefore, the 32nd term of the sequence 3, 18, 33, 48 is 468.