Question

Find the sum of natural numbers between 602 and 902 which are not divisible by 5​

Answer 1

Answer:

602,603,604,605,606,607,608,609,610,611,612,…,896,897,898,899,900,901,902

These are 301 given natural numbers (902–602+1 = 301)

Count the multiples of 4 which are in bold type (easy enough if we count how many by dividing each by 4;

These are 151,152,…,222,225 which are 75 entries)

So 604,608,…,896,900 are also 75 entries. They form an A.P. with first term a = 604, last term l = 900, number of terms n = 75

Their sum = (n/2)(a + l) = (75/2)(604 + 900) = 75 x 752 = 300x188 = 56400

Next sum of all the given numbers = (301/2)(602+902)=301(1504/2)=301x752= 225600+752=226352

Hence required sum = 226352 - 56400 =169952

Answer 2

Answer:

Sum of natural numbers not divisible by 5 = 180600

Step-by-step explanation:

Sum of natural numbers not divisible by 5 = Sum of natural numbers - Sum of natural numbers divisible by 5

Sum of natural numbers between 602 and 902:

603, 604, 605,.......901, 902

a = 603

l = 902

d = 1

n = (l - a)/d + 1

= (902-603)/1 + 1

= 299 + 1

n = 300

Sn = n/2[2a + (n - 1)d]

S300 = 300/2[1206 + 299]

= 150 [ 1505]

S300 = 225750

Sum of natural numbers divisible by 5:

605,610,.......900

a = 605

l = 900

d = 5

n = (l - a)/d + 1

= (900 - 605)/5 + 1

= 295/5 + 1

= 59 + 1

n = 60

Sn = n/2[2a + (n - 1)d]

S60 = 60/2[1210 +59×5]

= 30[1210 + 295]

= 30[1505]

S60 = 45150

Sum of natural numbers not divisible by 5 = Sum of natural numbers - Sum of natural numbers divisible by 5

= 225750 - 45150

Sum of natural numbers not divisible by 5 = 180600

Hope it helps you:)