Question

If 20 times of the 20th term of an A.P is equal to 11 times of the 11th term then find the 31st term.

Answer 1

Step-by-step explanation:

There is an example in the attachment

Answer 2

The 31st term is 0.

Given,

An AP has -

20a₂₀ = 11a₁₁

To Find,

31st term

Solution,

The general term of an AP is given as -

Tₙ = a + (n - 1)d

20a₂₀ = 11a₁₁

20 (a + 19d) = 11 (a + 10d)

20a + 380d = 11a + 110d

9a = - 270d

a = -30d

a₃₁ = a + (31 - 1)d

a₃₁ = a + 30d

As derived above a = -30d

a₃₁ = -30d + 30d

a₃₁ = 0

Thus, we get the 31st term as 0.

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