Question

If the numbers n – 2, 4n – 1 and 5n +2 are in AP, then the value of n is:

Answer 1

Answer:

Step-by-step explanation:

to understand A.p,

if a,b and c are in A.P

let a2 = b , a1 = a , a3 = c

As we know common difference = a2 - a1 , a3 - a2 and so on ..

AP is a, b , c

Common difference is same .

b -a = c - b

b +b = c + a

2b = c + a

then , 2b = a + c

similarily ,

n – 2, 4n – 1 and 5n +2 are in A.P

so,

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

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

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

8n - 2 = n - 2 + 5n + 2 (-2 and +2 gets cancelled)

8n - 2 = n + 5n

8n - 2 = 6n

8n - 6n = 2

2n = 2

n = 1

THEN THE VALUE OF n IS 2.

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