Question

Find the 10th term common between the series 3 , 7 , 11 ..... & 1 , 6 , 11, ....

CONTENT QUALITY REQUIRED.

Answer 1

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Answer 2

Answer : 

For first series  3  +  7  +  11  + 

We get that   7 - 3  =  11 - 7   = 4 
So,

Next term of that series will be As :

3  + 7 + 11  + 15  + 19 + 23  + 27  + 31  + 35  + 39  + 43  + 47 + 51  + ..... 

And fro second series 

1  + 6  + 11 + ..

We get that   6 - 1 = 11 - 6  =  5

So, Our next terms will be as  :

1  +  6  +  11  +  16  +  21  +  26  + 31  +  36  + 41  + 46  +  51  + .... 

Now get get that in both series , we have common 

11   ,  31  and 51  ... 

And 

31   -  11   =   51  -  31   =  20 

So 10th Common term that comes in both series will be the 10th term of our series ( 11  , 31   ,  51  , ... )

We know formula of nth term in A.P. 

t​n  =  a  + ( n  -  1 )  d

here a  = 11   , n  =  10  and d   =  20 So,

⇒t10  =  11 + ( 10  - 1 ) 20 

⇒t10 =  11 + (  9 ) 20 

⇒t10 =  11 + 180 

⇒t10 =  191 

So,

10th term that will be common in both given series , will be  =  191                      (  Ans )