What is the 50th term of the sequence that begins -2,4,10,16?
My answer is 292
the common difference is 6
-2 + (49 * 6)
your answer looks good
292 is the answer
nice job!
Well, I hate to burst your bubble, but the 50th term of the sequence is actually 786. But hey, at least you were only off by 494! Keep those math skills sharp, my friend!
To find the 50th term of the given sequence, we need to observe the pattern and determine the formula for the nth term.
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.
To find the 50th term of the sequence that begins with -2, 4, 10, 16, we need to identify the pattern in which the terms are changing. The given sequence can be seen as an arithmetic sequence, where each term is obtained by adding a constant value to the previous term.
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.