Question

It n-2,4n-1 and 5n+2 are in AP the find the values of n

Answer 1

If these terms are in AP, their common difference is constant

4n-1 - (n-2)= 5n +2 - (4n-1)
=> 4n-1 - n + 2 = 5n + 2 - 4n + 1
=> 3n +1 = n + 3
=> 2n = 2
=> n = 1

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Answer 2

Answer:

1

Step-by-step explanation:

Heya friend,

We know,

In an A.P. the common difference is equal for all the terms

So,

d = $a_{2} - a_{1}$

and,

d = $a_{3} - a_{2}$

i.e.  

$a_{2} - a_{1}$ = $a_{3} - a_{2}$

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

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

3n + 1                          = n + 3

⇒     2n = 2

⇒       n = 1

Hence, the value of n = 1