Question

when AP whose 11 term is 38 and 16 term is 73

Answer 1

Hey dear !!

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===>>> Given data

11th term = 38

16th term = 73

t₁₁ = a + 10d

38 = a + 10d

a + 10d = 38 .......................(1)

t₁₆ = a + 15d

73 = a + 15d

a + 15d = 73 .........................(2)

Now,subtract equation (2) from (1)

a + 15d = 73
a + 10d = 38
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5d = 35

d = 35/5

d = 7

Put d = 7 in equation (1)

a + 10d = 38

a + 10 x 7 = 38

a + 70 = 38

a = 38 - 70

a = -32

a = t₁

∴ t₁ = -32

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t₂ = t₁ + d

t₂ = -32 + 7

t₂ = -25

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t₃ = t₂ + d

t₃ = -25 + 7

t₃ = -18

Therefore, The A.P is -32,-25,-18......

Thanks !!