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AP the sum of integers from 1 to 100 that are devisible by 2 or 5 is
Asked by thakuranurag0987 | 27 Dec, 2022, 02:31: PM
Sum S of arithmetic progression is given as

where  n is number of terms in series , a is first term and d is common differnce .

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Let S2 be sum of integers from 1 to 100 that are divisble by 2

S2 = 2 + 4 + 6 + ..................................................+98 + 100   .........................(1)

There are 50 terms in above series.

S2 = ( 50 /2 ) [ 4 + (49 × 2) ] = 2550

Let S5 be sum of integers from 1 to 100 that are divisble by 5

S5 = 5 + 10 + 15 + .....................95 + 100   ................................(2)

There are 20 terms in above series.

S5 = ( 20 /2 ) [ 10 + (19 × 5) ] = 1050

common terms in both the series given by eqn.(1) and (2) are

S10 = 10 + 20 + 30 ......................+90+100

There are 10 terms in above series

S10 = (10/2) [ 20 + 9 × 10 ]  = 550

Sum S of numbers from 1 to 100 that are divisible by 2 or 5 is

S = S2 + S5 - S10 =  2550 + 1050 - 550 = 3050
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