In an Ap 19th term is 52 and 38th term is 128, find sum of first 56 terms
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a19 = 52
a+18d = 52 __ eq(i)
a38 = 128
a+37d = 128 __ eq(ii)
On subtracting eq(i) from eq(ii) we get
19d = 76
d = 76/19
d = 4
Replacing d=4 in eq(i),
a + 18(4) = 52
a +72 = 52
a = -20
s56 = 56/2 (2a + (n-1)d)
s56 = 28 (2(-20) + 55(4))
s56 = 28 (-40 + 220)
s56 = 28 (180)
s56 = 5040
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