Question

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Answer 1

Which answer do you want 6 or 7?

Answer 2

A.P=100,105,110,………..,995

Therefore,a=100

d=5

a+(n-1)d=995

100+(n-1)(5)=995

(n-1)(5)=895

(n-1)=179

n=180

Therefore ,there are 180 three digit numbers which are divisible by 5

First term ( a ) = ?

Common difference ( d ) = ?

11th term = 16

21st term = 29

Now,

 Nth term = First term + ( No. of terms - 1 )Common difference

11th term = a + ( 11 - 1 ) d

16 = a + 10d.

a = 16 - 10d    ----- ( 1 ).

Again,

Nth term = First term + ( No. of terms - 1 )Common difference

21st term = a + ( 21 - 1 )d

29 = a + 20d

29 - 20d = a  ------ ( 2 )

From ( 1 ) and ( 2 ), we get ,

29 - 20d = 16 - 10d

29 - 16 = 20d - 10d

13 = 10d

d = 13 / 10 = 1.3

By substituting the value of 'd' in ( 1 ),

a = 16 - 10d

a = 16 - 10 x 1.3

a = 16 - 13

a = 3.

Now,

Nth term = First term + ( No. of terms - 1 ) Common difference

41st term = 3 + ( 41 - 1 ) 1.3

                = 3 + ( 40 ) 1.3

                = 3 + 52

                = 55.