HOW TO FIND SUM OF ALL INTEGERS BETWEEN TWO NUMBERS

Example 1 :

Find the sum of first 40 positive integers divisible by 6. 

Solution :

By writing the positive integers which are divisible by 6, we get 

6, 12, 18, 24, ................ 40 terms

First term  =  6, common difference  =  6

Number of terms (n)  =  40

Sn  =  (n/2) [2a + (n - 1)d]

S₄₀  =  (40/2) [2(6) + (40 - 1)(6)]

  =  20 [12 + 39(6)]

  =  20 [12 + 234]

  =  20(246)

  =  4920

Example 2 :

Find the sum of first 15 multiples of 8.

Solution :

By writing the multiples of 8 as sequence, we get

8, 16, 24, 32, .............. 25 terms

First term  =  8, common difference  = 8

Number of terms (n)  =  25

Sn  =  (n/2) [2a + (n - 1)d]

S₂₅  =  (25/2) [2(8) + (25 - 1)(8)]

  =  (25/2) [16 + 24(8)]

  =  (25/2) [16 + 192]

  =  (25/2)(208)

  =  25(104)

=  2600

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