3016÷13 help.me please
2 answers:
Answer:
232.
Step-by-step explanation:
How many times can 13 go into 3? None. So we include the next digit.
How many times can 13 go into 30? 2 times. That's 26.
Subtract 26 from 30 = 4
Bring down the 1
How many times can 13 go into 41? 3 times. That's 39.
Subtract 39 from 41 = 2.
Bring down the 6.
How many times can 13 go into 26? 2 times!
Subtract 26 - 26 = 0
aaand you're done! The answer is 232. I've attached an image of how this would look written out. Sorry for the shakey handwriting, I haven't had breakfast yet.
Good luck!
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The easy thing to do is notice that 1^4 = 1, 2^4 = 16, 3^4 = 81, and so on, so the sequence follows the rule . The next number would then be fourth power of 7 plus 1, or 2402.
And the harder way: Denote the <em>n</em>-th term in this sequence by , and denote the given sequence by
.
Let denote the <em>n</em>-th term in the sequence of forward differences of
, defined by
for <em>n</em> ≥ 1. That is, is the sequence with
and so on.
Next, let denote the <em>n</em>-th term of the differences of
, i.e. for <em>n</em> ≥ 1,
so that
etc.
Again: let denote the <em>n</em>-th difference of
:
etc.
One more time: let denote the <em>n</em>-th difference of
:
etc.
The fact that these last differences are constant is a good sign that for all <em>n</em> ≥ 1. Assuming this, we would see that
is an arithmetic sequence given recursively by
and we can easily find the explicit rule:
and so on, up to
Use the same strategy to find a closed form for , then for
, and finally
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and so on, up to
Recall the formula for the sum of consecutive integers:
and so on, up to
Recall the formula for the sum of squares of consecutive integers: