Maybe you could look at it that way:
a=2+4+6+...+20 ==> you have 10 even integers
b=1+3+4+...+19==> you have 10 odd integers
a-b=(2-1)+(4-3)+(6-5)+...+(20-19)==> each term is 1 and you have 10 terms. Answer 10.
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Unfortunately, I am not able to follow your method... so can't comment..
I will suggest this would be easier...
a = 2+4+6.... +20
b= 1+3+5+....+19
a-b = (2+4+6.... +20)-(1+3+5+....+19) = 1+1+1.. (10 ones) = 10
You can also using Arithmetic Progression formula...
I will suggest this would be easier...
a = 2+4+6.... +20
b= 1+3+5+....+19
a-b = (2+4+6.... +20)-(1+3+5+....+19) = 1+1+1.. (10 ones) = 10
You can also using Arithmetic Progression formula...
why wont the short cut work
(largest +smallest)/2 for both sequences, to get avg of the sequence
largest -smallest +1 to get number of terms
times the two, avg times the number of terms to get the sum
eg
1, 2,3,4,5
1+5=6/2=3
3*5=15 same as 1+2+3+4+5=15
number of terms= 5-1+1=5.
Thanks
Khurram
(largest +smallest)/2 for both sequences, to get avg of the sequence
largest -smallest +1 to get number of terms
times the two, avg times the number of terms to get the sum
eg
1, 2,3,4,5
1+5=6/2=3
3*5=15 same as 1+2+3+4+5=15
number of terms= 5-1+1=5.
Thanks
Khurram
aatech
I like your thinking also. diff between each term is 1. so in toal 10 diff between the two.
I like your thinking also. diff between each term is 1. so in toal 10 diff between the two.
got it
was thinking consecutive not even set and odd set
thanks
khurram so my method cannot be used as that is for consecutive set only
was thinking consecutive not even set and odd set
thanks
khurram so my method cannot be used as that is for consecutive set only
No, the shortcut can still be used as it's still a consecutive set:khurram wrote:got it
was thinking consecutive not even set and odd set
thanks
khurram so my method cannot be used as that is for consecutive set only
sum of set= median x number of terms
2-20(e):
median= (20+2)/2 = 11
# terms= 10
sum= 110
1-19(o):
median= (19+1)/2= 10
# terms= 10
sum= 100
110-100= 10.
