Question

Solve the ques .... but without using A.P. concept....

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Answer 1

Answers :-

1) 2001

2)2001

Concept :-

Basic Arithmetic Progressions.

Given:-

1) a= 1000,d=1,An= 3000---> Question(1)

2) a= 1000,d=1,An=3000----> Question (2)

Series Between:-

1) 999 ... 3000

2) 99 ... 3000

Formula used :-

(1) N-th term of A.P

(2) N-th term of A.P

Ultimately,both will follow same steps, same formula.

Step By Step Explaination :-

Question(1):-

Series - 999 ... 3000

First 4 digit term will be 1000 this is will be "a".

Commin difference (d) = 1, since no. will be repeated each after one.

And the last term given is 3000

Using formula,

→ An= a+(n-1)d

→3000= 1000+(n-1)(1)

→3000-1000= n-1

→2000+1=n

→2001=n

=> now in question number (2).

Question(2):-

Series - 99 ... 3000

First 4 digit term will be 1000 this is will be "a".

Commin difference (d) = 1, since no. will be repeated each after one.

And the last term given is 3000. Same like above.

Using formula again :-

Using formula,→ An= a+(n-1)d

=> 3000=1000+(n-1)(1)

=> 2000+1=n

=> n= 2001

So, the number of terms, In thr series

1) 999 ... 3000 and

2) 99 ... 3000

Is same as 2001.

So, 2001 are the number of terms in both the series having four digits.

Ans.

Answer 2

Answer:

2000 is right answer for both questions.