Question

1.
Find the sum of integers between 200 and 300
that are
(0) Divisible by 13
(ii) Not divisible by 13​

Answer 1

Answer:

200/13 = 15.x

So the smallest integer above 200 is 13×16 = 208

300/13 = 23.x

So the largest integral below 300 is 13×23 = 299

Also the number of divisible from 13 is 23–16+1= 8

All of the multipliers of 13 are in arthimatic progression whose first term a= 208 and common difference is d= 13 and number of terms is n = 8

So sum of all divisibles of 13 btw 200 and 300 is

N/2( a + l)

= 4( 208+299)= 4×507 = 2028 ________ value 1

Now sum of all intergers between 200 and 300 is

200,201,202……………249

+300,299,298…………..251

+250

= 500 × 50 +250 =25250 ___________value 2

If we subtract value 1 from value 2,we would get Sum of all int btw 200 and 300 that are not divisible by 13

Ans is 25250- 2028 = 23222

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Answer 2

Answer:

First after 200 which is divisible by 13 = 208 (a)

2 term = 221

the difference = 221-208 = 13 (d)

Last term which is before 300 = 299 (aₓ)

A.P = aₓ = a+(n-1)d

299 = 208+(n-1)13

91 = (n-1)13

7 = n-1

8 = n

So now the sum of the 8 terms:

Sₓ = n/2 (a+aₓ)

S₈ = 8/2 (208+299)

= 4*507

=2028

Step-by-step explanation:

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