Question

Is the number n-2, 4n-1 and 5n+2 are
consecutive terms in AP. Find the value
of n​

Answer 1

Answer:

n = 1

Step-by-step explanation:

Arithmetic Progression :

• It is the sequence of numbers such that the difference between any two successive numbers is constant.

• General form of AP,

       a , a+d , a+2d , a+3d , ..........

Given,

⇒ n - 2 , 4n - 1 and 5n + 2 are in A.P

Let

a₁ = n - 2

a₂ = 4n - 1

a₃ = 5n + 2

Since they are in A.P., the difference between the successive numbers is constant.      

   a₂ - a₁ = a₃ - a₂

4n - 1 - (n - 2) = 5n + 2 - (4n - 1)

4n - 1 - n + 2 = 5n + 2 - 4n + 1

 3n + 1 = n + 3

 3n - n = 3 - 1

   2n = 2

     n = 2/2

     n = 1

The value of n is 1

Verification :

• Put n = 1,

➙ a₁ = n - 2

➙ a₁ = 1 - 2

➙ a₁ = -1

➙ a₂ = 4n - 1

➙ a₂ = 4(1) - 1

➙ a₂ = 4 - 1

➙ a₂ = 3

➙ a₃ = 5n + 2

➙ a₃ = 5(1) + 2

➙ a₃ = 5 + 2

➙ a₃ = 7

⇝ the difference of a term and the preceding term is same

 i.e., 3 - (-1) = 7 - 3 = 4

they're in AP

Hence verified!