Question

If the numbers n-2,4n-1and 5n+2 are in AP,find the value of n?

Answer 1

Answer:

The terms are n - 2, 4n -1 and 5n + 2.

We know that if a , b and c are in A.P. then =b

i.e. average of a and c is equal to b.

Therefore, by the condition:

=4n - 1.

⇒=4n -1

⇒=4n-1

⇒3n=4n-1

⇒4n-3n=1

⇒n=1

Ans:The value of n is 1 and the numbers are 1-2 = -1 , 4*1-1=3 and 5*1+2 = 7 respectively as we see that -1+4=3 and 3+4=7.

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