Question

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

Answer 1

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:)

Answer 2

Answer:

the first step is you have to find the sum of all no. from 602 to 902

a= 602 , d = 1 , tn = 902

tn = a+ ( n-1 ) d

902 = 602 + (n - 1) 1

902-602 = n-1

300 = n-1

n = 299

there fore

s299 = n/2 ( 2a + ( n-1 ) d)

s299 = 299/ 2 ( 2 x 602 + (299- 1 ) 1)

s299 = 299/2 ( 1204 + 298)

s299 = 299 / 2 x 1502

s299= 224549

and then find the summulation that is divisible by 5 from 602 to 902

a= 605 d = 5 tn = 900

tn = a+ ( n-1 ) d

900 = 605 + ( n-1) 5

900 - 605 = (n-1) 5

295 / 5 = n-1

59 +  1 = n

n= 60

s60 = n/2 ( 2a + (n-1) d)

s60 = 60 /2 ( 2x 605 + ( 60-1 ) 5 )

s60 = 45150

subtract both

224549 - 45150 =179339 is the sum off natural numbers not divisible by 5

thanks for my answer