An important question from ML Agarwal of Class10 We have asked If the numbers n-2, 4n-1 and 5n+2 are in AP, find the value of n?

Class 10 ML Agarwal Arithmetic Progression chapter 9 question no 21

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

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## n−2,4n−1,5n+2 are in A.P.

First term, a1=n−2

Second term, a2=4n−1

Third term, a3=5n+2

Common difference (difference of two consecutive terms),

d=a2−a1=a3−a2

4n−1−(n−2)=5n+2−(4n−1)

4n−1−n+2=5n+2−4n+1

3n+1=n+3

2n=2

n=1

So,

a1=n−2=1−2=−1

a2=4n−1=4−1=3

and d=a2−a1=3−(−1)=4

nth term of an AP is ,

an=a+(n−1)d

where,

a=first term

d=common difference

Therefore,

a4=a+3d=−1+12=11

a5=a+4d=−1+16=15