A sequence is numbers is written in the following position : 1,7,1,1,7,7,1,1,1,7,7,7, ------- till n terms

what is the value of \left (T _{5040} \right +T_{5042}+T_{5044}+T_{5046})

T_{n} is the nth term of the given sequence.

  • Option 1)

    4

  • Option 2)

    28

  • Option 3)

    10

  • Option 4)

    22

 

Answers (1)

As learnt in concept

Sequence -

Arragement of real numbers specified in a definite order, by some assigned law.

- wherein

Notations -

a_{1},a_{2},a_{3},a_{4}.........a_{n}

or

< a_{n}>

 

 

The number of terms that end are ;

2, 2+4, 2+4+6, 2+4+6+8.....

So we get, 

2+4+6+8+....+n terms

=2*n*\frac{n+1}{2}= n(n+1)

Now, 

T_{4970}= 7

Then,

T_{5040}= 1

and rest of the terms, T_{5042}= T_{5044}=T_{5046}= 7

So,

Sum= 22 


Option 1)

4

Incorrect option

Option 2)

28

Incorrect option

Option 3)

10

Incorrect option

Option 4)

22

correct option

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