If the middle term of the AP is 300 , then the sum of its first 51 terms is

Step-by-step solution

Given, number of terms, n=51 n is odd. Middle term will be ( n+1 2 ) th term. aligned &= ( 51+1 2 ) th term =26 th term & T₂₆=300 aligned a+25 d=300 [ T_ n =a+(n-1) d ] T₁+25 d=300 [ T₁=a ]T₁=300-25 d and T₅₁=a+50 d=T₁+50 d=300-25 d+50 d=300+25 d S₅₁= 51 2 [300-25 d+300+25 d] = 51 2 [600]=15300