Question

Find the sum of all natural no from 1 to 50 which are not divisible by 3

Answer 1

Find the difference between(sum of natural numbers from 1 to 50 and sum of numbers that are divisible by 3 from 1-50)

Sum of natural numbers from 1 to 50
n*(n+1)/2 = 50*51/2 = 1275

Sum of multiples of 3 from 1 to 50
3,6,9...48
 Sum of A.P = n/2 ( A1 + An)
An = A1 + (n-1)*d
48 = 3 + (n-1)*3
45 = (n-1)*3
n-1 = 15
n = 16
Sum = 16/2*(3+48) = 51*8 = 408

Hence sum of all the numbers from 1 to 50 which are not divisible by 3 is:
1275 - 408 = 867

Hope it helps

Answer 2

No/s Divisible by 3

3, 6, 9, 12, ............ 48

From the AP:

l = 48  ;  a = 3  ;  d = 3 

Then l = a + (n-1)d

    48 = 3 + (n-1)3

    45 = (n-1)3

(n-1) = 45/3

      n = 16 terms,
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Then AP' : 1, 2, 3, 4, .........., 50

From the AP' : 

l' = 50  ;  a' = 1  ;  d' = 1

Then  l' = a' + (n'-1)d'

      50 = 1 + (n'-1)1

      49 = (n'-1)

       n' = 50 terms.
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From the above answers,

Sum of natural no/s not divisible by 3 = Sum of natural no/s - Sum of

                                                                    natural no/s divisible by 3
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Sum of natural no/s = n'/2 (a'+l')

                                = 50/2 (1+50)

                                = 1275.
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Sum of natural no/s divisible by 3 = n/2 (a+l)

                                                      = 16/2 (3+48)

                                                      = 408
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Sum of natural no/s not divisible by 3 = 1275 -  408

                                                            = 867
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