Q. 164.0( 4 Votes )

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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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