Question

In an Ap 19th term is 52 and 38th term is 128, find sum of first 56 terms

Answer 1

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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