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Average of first n even numbers

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Even numbers are 2,4,6,8,10,…. Average = sum of elements/ no of elments Now we will see the sum of elements: Sum of first 2 even numbers: 2+4= 6= 2(2+1) Sum of first 3 even numbers: 2+4+6= 12= 3(3+1) Sum of first 4 even  numbers: 2+4+6+8=20= 4(4+1) Sum of first 5 even numbers: 2+4+6+8+10 = 30 = 5(5+1) Sum of first n even numbers: 2+4+6+8+10+. . . . .  n numbers= n(n+1) Now we will see average: Average of first 2 even numbers= (2+4)/2                                                           = 6/2                              ...
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sum of even numbers from 2 to 100

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Even numbers from 2 to 100 Even numbers are 2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,    54, 56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,98,100. Now we will see the sum of elements: Sum of first 2 even numbers: 2+4= 6 The above can be written as Sum of first 2 even numbers: 2+4= 6= 2x3=2(2+1) Sum of first 3 even numbers: 2+4+6= 12= 3(3+1) Sum of first 4 even  numbers: 2+4+6+8=20= 4(4+1) Sum of first 5 even numbers: 2+4+6+8+10 = 30 = 5(5+1) Sum of first n even numbers: 2+4+6+8+10+. . . . .  n numbers= n(n+1) Sum of  even numbers from 2 to 100 = 2+4+6+8+10+. . . . .  50 numbers                                                                           = 50(50+1)           ...
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how many times a day do the minute and hour hands of a clock form a straight line but in opposite direction

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For this I am not writing any formula , simply  with the help of table we will try to understand the concept. the minute and hour hands of a clock form a straight line but in opposite direction 1 Between 12.30 to 12.35 2 Between 1.35 to 1.40 3 Between 2.40 to 2.45 4 Between 3.45 to 3.50 5 Between 4.50 to 4.55 6 Between 5.55 to 6.00  : means at 6.00 clock they are straight but opposite @ Between 6.00 to 6.05 hands are not straight in opposite direction 7  Between 7.05 to 7.10 8 Between  8.10 to 8.15 9 Between  9.15 to 9.20 10 Between  10.20 to 10.25 11 Between  11.25  to 11.30                  #  goto step 1 @ in 6 th column if we see in 5 to 6 hours and 6.00 to 7.00 hours t...
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