Bunuel wrote:
stne wrote:
some one please enlighten me
please list the whole series and how a common difference of -4 is obtained .
Sorry my limited wisdom is unable to grasp the process
as far as I can see the terms are decreasing by 2 with alternating + and - sign
so the series should continue as 10 -8 +6 - 4 + 2 - 0 + (-2) - ( -4 ) + ( -6) - (-8 ) + ( -10) -( -12) +( -14 )
- (-16) +(-18)- (-20)
10 - 8 + 6 - 4 + 2 - 0 -2 + 4 - 6 + 8 - 10 + 12 - 14 + 16 - 18 + 20
some one please explain how common difference is - 4
please include the complete series so that we can see how this works
Here you go:
The sequence is \(10-8+6-4+2-0+(-2)-(-4)+(-6)-(-8)+(-10)-(-12)+(-14)-(-16)+(-18)-(-20)\).
Notice that the odd numbered terms (1st, 3rd, 5th...) form arithmetic progression with common difference of -4 and the even numbered terms (2nd, 4th...) form arithmetic progression with common difference of 4:
The sum of the odd numbered terms is \(10+6+2+(-2)+(-6)+(-10)+(-14)+(-18)=10+6+2-2-6-10-14-18=
16\);
The sum of the even numbered terms is \(-8-4-0-(-4)-(-8)-(-12)-(-16)-(-20)=-8-4-0+4+8+12+16+20=48\);
Their sum is \(-32+48=16\).
Though I wouldn't recommend to solve this question this way. It's better if you notice that we have 8 pairs:
10-8=2;
6-4=2;
2-0=2;
(-2)-(-4)=2;
(-6)-(-8)=2;
(-10)-(-12)=2;
(-14)-(-16)=2;
(-18)-(-20)=2;
So, the sum of each pair is 2, which makes the whole sum equal to 8*2=16.
Hope it's clear.
Thank you , now the previous explanations make sense
Just a small typo in your answer , I think it should be - 32 instead of 16 ( addition of odd terms ) , please do edit , to prevent confusion.
I was not able to see that even and odd terms are making an AP .
as Kudos is a better way of saying thank you , so you have been awarded , will be needing more of your assistance
in the future
_________________