An AP consists of 43 terms. If the sum of 5 middle most terms is 195 then what is the sum of the AP?

Dear student, ACQ, sum of 21st,22nd and 23rd term is 195 , i.e a+20d + a+21d + a+22d = 195 ,that implies a + 21d = 65 sum of the AP = n(2a + (n-1)d)/2 = 43( 2a + 42d)/2 = 43(a+21d) = 43(65) = 2795. Regards

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number of terms 43
middle term is 22
thus 5 middle terms are 20th-24th
a20 + a21 + a22 + a23 + a24 + a25 = 195

a + 19d + a + 20d + a +21d + a + 22d + a + 23d + a + 24d = 195
5a + (19+20+21+22+23)d = 195
5a + 105d = 195
5(a+21d) = 195
a + 21d = 39
S43 = (43/2)( 2a + 42d)
S43 = 43(a+ 21d) = 43*39 =  1677
 
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