Find the value of 1 -3 + 4 - 6 + 7 - 9 + 10 - ... - 300 + 301
Really not sure how to do this
if you put it in brackets like this: (1-3) + (4-6) + (7-9) .....
you can see that it is one -2 every 3 numbers: (-2) + (-2) + (-2) ...
if we now go up to -300 we have: -2 * 100 = -200
now u only need to add the 301 to the -200: -200 + 301 = 101
so the solution is 101.
+9665 1-3+4-6+7-9+10-....-300+301
I will code it like
| Number | Code |
| 1 | 1 |
| -3 | 2 |
| 4 | 3 |
| -6 | 4 |
Look at the numbers with odd-numbered code which I have already bolded.
The numbers of code with the form 2n+1 are with the form of 3n+1.
Look at the numbers with even-numbered code which I set the font Italic.
The numbers of code with the form 2n are with the form 3n.
1-3+4-6+7-9+10-....-300+301
= (1+4+7+10+......+301)-(3+6+9+......+300)
There are \(\color{blue}\frac{301-1}{4-1}+1\) terms in (1+4+7+10+......+301)
which is 101 terms.
There are \(\color{blue}\frac{300-3}{6-3}+1\) terms in (3+6+9+......+300)
which is 100 terms.
1-3+4-6+7-9+10-....-300+301
= (1+4+7+10+......+301)-(3+6+9+......+300)
= \(\color{blue}\frac{(1+301)(101)}{2}-\frac{(3+300)(100)}{2}\)
=303 <------ Final Answer
+129839 Split this up as two separate series
1 + 4 + 7 + 10 +....+ 301 and
-3 - 6 - 9 - 12 -.....- 300
The number of terms in the first series can be found as follows :
301 = 1 + (n - 1)3
300 = (n - 1)3
100 = n - 1
n = 101
So.....the sum of the first series =
(101)(1 + 301)/2 = 15251
The number of terms in the second series can be found as follows:
-300 = -3 - 3(n - 1)
-297 = -3(n - 1)
99 = n - 1
n = 100
So.......the sum of this series =
(100)(-3 + -300)/2 = - 15150
So......the sum of the two series = 15251 - 15150 = 101
