Question

Find sum of all odd numbers between 0-50

Answer 1

1+3+5+7+9.......99..there are 50 no.
USE Arithmetic progression formula
a=1 common difference =2  
sum of 50 terms=(first term +last term) X no . of terms/2
=>(1+49)*25/2
25*25=625

Answer 2

Heya user,

We have to find --> [ 1 + 3 + 5 + ... + 49 ]

Hence, this is equal to ---> [ ( 0+1 ) + ( 2 + 1 ) + ... + ( 48 + 1 )
= [ 1 + 1 + ... + 25 times ] + [ 2 + 4 + ... + 48 ]
= 25*1 + 2 [ 1 + 2 + ... + 24 ]
= 25 + 2 [ 300 ] 
= 25 + 600 = 625...

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Another soln. is --->

We know, the sum of 'n' odd integers = n²
So, here, [ 1 + 2 + ... + 49 ] = sum of 25 odd integers = 25² = 625

Hence, we get the result as 625;

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Or else, we can use the formula for sum of AP where a = 1; c.d. = 2

Hence the sum of 25 terms = 25/2 * [ 2a + ( 25 - 1 )c.d. ]
= 25/2 * [ 2 + 24*2 ]
= 25 * 25 = 625;

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