Q. 164.0( 4 Votes )

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Answer :

nth term of an A.P. is given by an=a + (n-1)d

Given: a=-6; d=-2-(-6) =4; an=58


Substituting the values of a and d in the formula of an


a + (n-1)d=58


(-6) + (n-1)4=58


(n-1)4=58 + 8=64
n-1=64/4=16


n=17


We see that n is odd.


So,Middle term=th term==9th term


Middle term = a + (n-1)d =( -6) + (9-1)4=(-6) + 32=26


Or


Let us assume that,


First term of A.P.=a


Common difference=d


We know that nth term of an A.P. is given by an=a + (n-1)d


4th term of A.P.= a + 3d =18(given)…….(1)


Also, 15th term – 9th term =30


(a + 14d)-(a + 8d) =30


6d =30


d=5


Putting the value of d in equation 1


a + 3(5) =18


a + 15= 18


a= 3


So the A.P. is 3,8,13,18,23,28,33……..


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