Question

Find the sum of all numbers from 1-50 which are not divisible by 4

Answer 1

nos not divisible by 4 from 1-50 are

2,3,5,6,7,9,10,11,13,14,15,17,18,19,21,22,23,25,26,27,29,30,31,33,34,35,37,38,39,41,42,43,45,4647,49

sum=912

Answer 2

First AP : 4 , 8 , 12 , 16 , ...... , 48 .

a = 4

d = 8 - 4 = 4

aₙ = 48

n = ?

Sₙ = ?

aₙ = a + ( n - 1 ) d

48 = 4 + ( n - 1 ) 4

( n - 1 ) 4 = 48 - 4

( n - 1 ) = 44 / 4

n = 11 + 1

n = 12

Sₙ = n / 2 [ a + aₙ ]

Sₙ = 6 [ 4 + 48 ]

Sₙ = 6 [ 52 ]

Sₙ = 312

Second AP : 1 , 2 , 3 , 4 , ...... , 50 .

a = 1

d = 1

aₙ = 50

n = 50

Sₙ = 50 / 2 [ 1 + 50 ]

Sₙ = 25 [ 51 ]

Sₙ = 1275

∵ Sum of terms not divisible by 4 = 1275 - 312 = 963