Q10 of 47 Page 1

Find the middle term of the A.P. 213, 205, 197, …. 37.

The given A.P. is 213, 205, 197, …, 37


Let n be the number of terms,


Common difference, d=205-213=-8


First term, a=213


Last term, an=37,


an=a + (n-1)d


⇒ 37=213 + (n-1)(-8)


⇒(-176)=(n-1)(-8)


⇒22=n-1


⇒n=23(Odd)



So, we have to find a12 for this A.P.


a12=213 + (12-1)(-8)


⇒ a12=213 + 11 × (-8)


⇒ a12=213-88


⇒ a12=125


So, The middle term of this A.P. is 125.


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