What is the 50th term of the sequence that begins -6,0,6,12?
292
288
286
290
Figure out the rule of the sequence in terms of n, the number of terms
We have common difference =6
T(0)=-12
T(1)=-6
T(2)=0
T(3)=6
Let's try
T(n)=-12+6n
so T(1)=-12+6=-6
T(2)=-12+6*2=0
T(3)=-12+6*3=6,...
It works.
So
T(50)=-12+50*6=288
Well, let me take a crack at it and see if I can put a smile on your face!
If we take a closer look at the sequence, we can see that the difference between consecutive terms is a constant 6. So, we can think of this sequence as an arithmetic progression with a common difference of 6.
To find the 50th term, we can use the formula for the nth term of an arithmetic progression, which is given by:
nth term = first term + (n - 1) * common difference
Plug in the values for the first term (-6), common difference (6), and the desired term number (50):
50th term = -6 + (50 - 1) * 6 = -6 + 49 * 6 = -6 + 294 = 288
So, it looks like the 50th term of the sequence is 288. I hope that answers your question and brings a smile to your face!
To find the 50th term of the sequence, we need to determine the pattern first. Looking at the sequence -6, 0, 6, 12, we can see that each term is obtained by adding 6 to the previous term.
Let's write out the terms of the sequence:
Term 1: -6
Term 2: -6 + 6 = 0
Term 3: 0 + 6 = 6
Term 4: 6 + 6 = 12
We can observe that each term is obtained by adding 6 to the previous term. So, we can generate the terms of the sequence using the formula:
Term n = Term 1 + (n - 1) * common difference
In this case, the term 1 is -6, the common difference is 6, and we want to find the 50th term:
Term 50 = -6 + (50 - 1) * 6
Term 50 = -6 + 49 * 6
Term 50 = -6 + 294
Term 50 = 288
Therefore, the 50th term of the sequence is 288.
To find the 50th term of a sequence that starts with -6, 0, 6, 12, we need to determine the pattern and use it to find the 50th term.
Looking at the given sequence, we can observe that each term is obtained by adding 6 to the previous term.
To find the 50th term, we can apply the formula for the nth term of an arithmetic sequence:
nth term = first term + (n - 1) × common difference
In our case, the first term is -6, the common difference is 6, and we want to find the 50th term, so n = 50.
50th term = -6 + (50 - 1) × 6
50th term = -6 + 49 × 6
50th term = -6 + 294
50th term = 288
Therefore, the 50th term of the given sequence is 288.