the series of odd numbers from 1 to 99 :1 3 5 7 9.....99
SUM OF THE SERIES:
It is a geometric progression with a=1 and l=99 and common difference (d)=2.
let 99 be the nth term of the sequence
so, 99=1+(n-1)d
99=1+(n-1)2
solving this we get n =50.
SUM=(n/2)(a+l)
=(50/2)(1+99)
=(25)(100)
=2500.
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100
2500
9801 * The sum of the first two odd numbers (1+3) is 4, or 22 * The sum of the first three odd numbers (1+3+5) is 9, or 32 * The sum of the first four odd numbers (1+3+5+7) is 16, or 42 * ...and so on So the sum of the first 99 odd numbers, using the pattern above, would be 992 or 9801.
97 and 99
let the number be n-1, n, n+1 then 3n=99 and so n=33 the numbers are 32, 33, 34