Question

find the middle term of the AP 11,15,19,.......................,139

Answer 1

An= 11+(139-1)4
=11+138*4
11+552
563



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Answer 2

Answer:

75

Step-by-step explanation:

given A.P. is starting with 11.

so here a=11 , d=4 , l=139

as we know last term is 139

so

$139=\frac{n}{2}[2*11+(n-1)*4\\\\139=\frac{n}{2}[22+4n-4]\\\\278=n[18+4n]\\\\4n^{2}+18n-278=0\\\\2n^{2}+9n-139=0$

by solving this we get n=33

so middle term will be 17th

as we know 55th term will be =a+(n-1)*d

=11+(17-1)*4

=11+16*4

=11+64

=75

so middle term will be 75.