Explanation
Given A.P is 13q,1−6q3q,1−12q3q
Since a3=a+2d,
To get a20 ,
Step -1: Write three digit multiple of 6 as A.P. having common difference as 6.
Multiple of 6 between 100 and 999 are as follows:
102,315,324,…,996
So, the formed A.P. is 102,315,324,…,996
Where, a=102: First term of A.P.
d=6: common difference of A.P.
l=996: Last term of A.P.
Now we know that, formula for nth term of an A.P. is given by,
an=a+(n−1)d…(1)
Where, a= First term of A.P.
d= common difference of A.P.
an= nthterm of an A.P.
n= Total number of terms in A.P.
Step -2: Substitute the known values in equation (1)
⇒996=102+(n−1)6
⇒996−102=(n−1)6
⇒894=(n−1)6
⇒(n−1)=8946
⇒n−1=149
⇒n=149+1
⇒n=150
Therefore, option B. 150 is correct answer.
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