Question

Find the middle term of an A.P 135,140,145,...,385

Answer 1

A.P 135,140,145,...,385

given,a=135 c.d=5

Let Tn be 385

Tn=a+(n-1)d

385=135+(n-1)5

385=135+5n-5

385=130=5n

385-130=5n

255=5n

255/5=n

51=n

51 is a odd no so middle term of this AP is n+1/2=51+1/2

=52/2

26

hence 26th term of AP will be its middle term.

T26=a+(n-1)d

=135+(26-1)5

=135+25×5

=135+125

=260

Hence,middle term of an A.P 135,140,145,...,385 is 260

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