Question

find the middle term of of the ap. 10,7,4,......,-62

Answer 1

Heya !!


AP = 10 , 7 , 4 ,........., -62



Here,


First term ( A ) = 10

Common difference (D) = 7-10 = -3



Tn = -62


A + ( n - 1 ) × D = -62



10 + ( n - 1 ) × -3 = -62



10 - 3n + 3 = -62




-3n = -62 - 13


n = -75/-3 = 25


Thus , the given AP contains 25 terms.



Therefore,


It's middle term = 1/2 × (25+1 ) = 13th term.



So, middle term = T12 = A + 11D




=> 10 + 11 × -3



=> 10 - 33


=> -23.



Hence,

the middle term is -23.
Hope it will help you :-)