Sum of observations = Average X Number of Observations
2. Average Speed: If a man covers a certain distance at X km/h and an equal distance at Y km/h. Then, the average speed during the whole journey is 
3. Consecutive even numbers (or) odd numbers = x, x+2, x+4, x+6 ..,,,
4. For a set of non-zero numbers, if we add/subtract/multiply/divide with some non-zero quantity, then the result average also increased/decreased/multiplied/divided by the same non-zero quantity.
5. Average of first 'n' natural numbers = (n+1)/2
6. Average of first 'n' odd numbers = n
Sum = n2
Ex: We take 1, 3, 5, 7, 9, then find their Average and Sum?
Sol: In the above question, there are first 5 odd numbers (i.e., n = 5)
Their Average = (1 + 3 + 5 + 7 + 9)/5 = 25/5 = 5
Sum = 1 + 3 + 5 + 7 + 9 = 25 (i.e., n = 5, n2 = 25)
7. Average of first 'n' even numbers = n + 1
Sum = n*(n + 1)
8. For Even (or) Odd numbers in sequence
First term = Average - (n - 1)
Last term = Average + (n + 1)
9. For consecutive natural numbers
First term = Average - {(n - 1)/2}
Last term = Average + {(n - 1)/2}
9. Sum of 'n' consecutive natural numbers = 1, 2, 3, .......n = {n * (n+1)}/2
10. Sum of squares of 'n' consecutive natural numbers = 12, 22, 32, .......n2
= { n*(n+1)*(n+2)}/6
11. Sum of cubes of 'n' consecutive natural numbers =13, 23, 33, .......n3
= { n2*(n+1)2}/4
(or)
= [{n*(n+1)}/2]2
No comments:
Post a Comment