the common difference is 6
-2 + (49 * 6)
your answer looks good
My answer is 292
-2 + (49 * 6)
your answer looks good
nice job!
From the given sequence -2, 4, 10, 16, we can observe that the sequence is increasing by 6 each time.
The formula for the nth term of an arithmetic sequence can be expressed as:
tn = a + (n - 1)d
where tn is the nth term, a is the first term, n is the position of the term, and d is the common difference.
In this case, the first term (a) is -2 and the common difference (d) is 6.
Using the formula, we can find the 50th term (tn) as follows:
t50 = -2 + (50 - 1) * 6
t50 = -2 + 49 * 6
t50 = -2 + 294
t50 = 292
Therefore, the 50th term of the sequence is 292.
If we look at the differences between consecutive terms, we can determine this constant value.
The differences between the terms are:
4 - (-2) = 6
10 - 4 = 6
16 - 10 = 6
Since the differences are constant and equal to 6, we can conclude that this is an arithmetic sequence with a common difference of 6.
Now, we can find the 50th term using the formula for the nth term of an arithmetic sequence:
An = A1 + (n - 1) * d
Where:
An refers to the nth term
A1 is the first term
n is the position of the term
d is the common difference
We know that A1 = -2, d = 6, and n = 50. Plugging these values into the formula:
A50 = -2 + (50 - 1) * 6
A50 = -2 + 49 * 6
A50 = -2 + 294
A50 = 292
Therefore, the 50th term of the sequence is indeed 292.