Q. 193.8( 27 Votes )

Find the sum of two middle most terms of the AP

Answer :

First term of the AP = - (4/3)

Common difference = d = - 1 - (-4/3) = - 1 + (4/3) = 1/3


Last term = 13/3


Since


an = a + (n - 1) × d


13/3 = (-4/3) + (n - 1) × (1/3)


(13/3) + (4/3) = (n - 1) × (1/3)


17/3 = (n - 1) × (1/3)


17 = n - 1


n = 17 + 1


n = 18


Two middle most terms of the AP are 18/2 and (18/2) + 1 terms, i.e. 9th and 10th terms.


So, a9 = a + (9 - 1) × d


a9 = (-4/3) + [8 × (1/3)]


a9 = (-4/3) + (8/3) = 4/3


Also, a10 = a9 + d


= (4/3) + (1/3)


= 5/3


Now, a10 + a9 = (4/3) + (5/3)


= 9/3


= 3


Sum of two middle most terms of the AP is 3.


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