Question

if the number n-2 , 4n-1 and 5n+2 are in AP , find the value of n​

Answer 1

If the numbers n-2, 4n-1 and 5n+2 are in A. P., what is the value of n?

First we find the common difference (CD) between first two terms of series

CD = 4n - 1 - (n - 2)

CD = 4n - 1 - n + 2

CD = 3n + 1

Again find the common difference between 4n - 1 and 5n + 2 as

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

CD = 5n + 2 - 4n + 1

CD = n + 3

In arthmetic progression (A.P), common difference between the terms must be same, therefore

3n + 1 = n + 3

3n - n = 3 - 1

2n = 2

n = 1 which is our answer

Putting n= 1 in above a. p series,

1–2 , 4×1 - 1 , 5×1 + 2

-1 , 3 , 7 are in A. P.

Answer 2

Step-by-step explanation:

n-2 + 4n-1 + 5n

a= n-1

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

= 3n+1 = n+3

= 2n= 2

n= 1