Question

If numbers n – 2, 4n – 1 and 5n + 2 are in A.P. find the value of n and its next two terms.

Answer 1

$\:The\: terms\: are\: n - 2\: , \: 4n -1 \: and\: 5n+2.\:$
We know that if a , b and c are in A.P. then \frac{a+c}{2}2a+c​ =b
i.e. average of a and c is equal to b.
Therefore, by the condition:
\frac{(n-2)+(5n+2)} { 2 }​ =4n - 1.
⇒\frac{6n}{2}26n​ =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.