Given:
The sequence is:
To find:
The explicit formula for the given sequence then find the 47th term.
Solution:
We have,
The difference between two consecutive terms are:
The given sequence has a common difference. So, the given sequence is an arithmetic sequence with first term -3 and common difference 8.
The explicit formula for an arithmetic sequence is:
Where, a is the first term and d is the common difference.
Putting and in the above formula, we get
Putting , we get
Therefore, the explicit formula for the given sequence is and the 47th term is 365.
Answer:
25 + m = 65
Step-by-step explanation:
Chas has 25 video games. Add to this the number the video games Tyler has which is m. This makes the expression 25 + m. This is equal to 65 games. So, the total number of video games is 25 + m = 65.
Answer:
870
Step-by-step explanation:
70
Answer:
15x^2 - 12x^3
Step-by-step explanation:
A rectangular block has 3 parts that play into its volume. length, width and height. The question gives us length and width in the form of x and 3x, so height is what's missing.
It gives us a bit more information saying the sum of its edges is 20. We also have to ask how many lengths, widths and heights are there. That may be a bit hard to understand, but is you are looking at a block I could ask how many edges are vertical, just going up and down. These would be the heights. There are 4 total, and this goes the same for length and width, so 4*length + 4*width and 4*height = 20.
Taking that and plugging in x for length and 3x for width (or you could do it the other way around, it doesn't matter, you get:
4*x + 4*3x + 4*height = 20
4x + 12x + 4h = 20
16x + 4h = 20
4h = 20 - 16x
h = 5 - 4x
Now we have h in terms of x, which lets us easily find the volume just knowing x. To find the volume of a rectangular block you just multiply the length, width and height.
x*3x*(5-4x)
3x^2(5-4x)
15x^2 - 12x^3
Question doesn't give a specific value for x at all so you should be done there. Any number you plug in for x should get you the right answer
I think the answer is C but im not sure