Question

plz help!
how 449 came?

Answer 1

= > The number divisible by 9 between 108 to 550 :

Here AP is 108,117...549.

a = 108, d = 117 - 108 = 9, an = 549.

= > an = a + (n - 1) * d

= > 549 = 108 + (n - 1) * 9

= > 549 = 108 + 109n - 9

= > 9n = 450

= > n = 50.

Sum of n terms = (n/2)[a + l)]

= > 50/2[108 + 549]

= > 25[657]

= > 16425. ----- (1)

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Now,

Sum of terms from 101,102....549

= > a = 101, d = 1, an = 549.

= > 549 = 101 + (n - 1) * 1

= > 448 = (n - 1)

= > n = 448 + 1

= > n = 449.

Now,

Sn = (449/2)[101 + 549]

= (449/2)[650]

= 449 * 325

= 145925 ----- (2)

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Now,

Sum of all integers which are not divisible by 9 are:

= > 145925 - 16425

= > 129500.

Hope this helps!