in an AP if the first term is 5 and the common difference is 2. if the last term is 53 find its middle term

Dear student
Given first term =a=5common difference=d=2last term of AP=53let there be n terms in given APan=53a+n-1d=535+n-12=53n-12=48n-1=24n=25The middle term is given byn+12th term=25+12=13termSo a13=a+n-1da13=5+24×2a13=53
Regards

  • 1
n=53+1/2=27
a=5 d= 2 n=27 
An= 5+(27-1)2
   =5+26 X 2
   =5+52
   =57
  • -1
Tn=a+(n-1)d
53=5+(n-1)2
48/2=n-1
n=25
Therefore,n+1/2
26/2
=13
so 13th is the term
T13=5+(13-1)2
       =5+(12)2
       =5+24
       =29
  • 4
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