n AM's are inserted between 2 and 38. If third AM is 14, then n is equal to

  • Option 1)

    9

  • Option 2)

    7

  • Option 3)

    8

  • Option 4)

    10

 

Answers (1)

As we learnt in 

Inserting n AMs between a and b -

a_{1},A_{1},A_{2},A_{3},A_{4},- - - - A_{n},b are in AP

- wherein

a is the first term 

b is the (n+2)th term of the AP.

 

 \\2,A_1,A_{2},A_{3},.......A_{n},38\\*\\*38=2+(n+1)d\\*\\*Also\, \, 14=2+3d= > d=4\\*\\*38=2+\left ( n+1 \right )4\\*\\*36=\left ( n+1 \right )4= > n=8


Option 1)

9

Incorrect

Option 2)

7

Incorrect

Option 3)

8

Correct

Option 4)

10

Incorrect

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