How to solve sum of series in quick way?
Let's take some questions
Find the sum of following series ?
1. 1,2,3,4,5,6........60
2. 21,22,23,24.... 75
3.2,4,6,8..............60
4.28,30,32,..........80
5.1,3,5,7..............69
6.23,25,27...........71
7. First 10 multiple of 3
Method
First find n=((last number-starting number)/difference ) +1 ,
Then sum=((last number+starting number)*n)/2
Answers of above questions
Ans 1: first number =1, last number=60, difference=2-1=3-2=4-3=1,
n=((60-1)/1)+1= 59+1=60,
Sum=((60+1)*60)/2=61*60/2= 61*30=1830,
Ans 2: Sum=((21+75)*55)/2=96*55= 48*55=2640
Ans 3: sum=((2+60)*30)/2=62*30/2=31*30=930
Ans 4: sum=((28+80)*27)/2=108*27/2=54*27=1458
Ans 5: sum=((1+69)*35)/2=70*35/2=35*35=1225
Ans 6: sum =((23+71)*25)/2=94*25/2=47*25=1175
Ans 7 : sum=((3+30)*10/2=33*10/2=33*5=165
Let's take some questions
Find the sum of following series ?
1. 1,2,3,4,5,6........60
2. 21,22,23,24.... 75
3.2,4,6,8..............60
4.28,30,32,..........80
5.1,3,5,7..............69
6.23,25,27...........71
7. First 10 multiple of 3
Method
First find n=((last number-starting number)/difference ) +1 ,
Then sum=((last number+starting number)*n)/2
Answers of above questions
Ans 1: first number =1, last number=60, difference=2-1=3-2=4-3=1,
n=((60-1)/1)+1= 59+1=60,
Sum=((60+1)*60)/2=61*60/2= 61*30=1830,
Ans 2: Sum=((21+75)*55)/2=96*55= 48*55=2640
Ans 3: sum=((2+60)*30)/2=62*30/2=31*30=930
Ans 4: sum=((28+80)*27)/2=108*27/2=54*27=1458
Ans 5: sum=((1+69)*35)/2=70*35/2=35*35=1225
Ans 6: sum =((23+71)*25)/2=94*25/2=47*25=1175
Ans 7 : sum=((3+30)*10/2=33*10/2=33*5=165
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