1.

10th and 20th term of a H.P are 1/5and 1/10 respectively.find the 40th term ​

Answer»

-Given:10th term of a HP = 1/520th term = 1/10 We KNOW that,HP is inverse of AP.So,10th term of an AP = 520th term = 10We know,nth term of an AP (aₙ) = a + (n - 1)DSO,★ a + (10 - 1)d = 5⟹ a + 9d = 5 -- equation (1).★ a + (20 - 1)d = 10⟹ a + 19D = 10 -- equation (2).Subtract equation (1) from equation (2).⟹ a + 19d - (a + 9d) = 10 - 5⟹ a + 19d - a - 9d = 5⟹ 10d = 5⟹ d = 5/10⟹ d = 1/2Substitute the value of d in equation (1)⟹ a + 9(1/2) = 5⟹ a = 5 - 9/2⟹ a = (10 - 9)/2⟹ a = 1/2Now,40th term of the AP = 1/2 + (40 - 1)(1/2)⟹ a₄₀ = 1/2 + 39/2⟹ a₄₀ = (1 + 39)/2⟹ a₄₀ = 40/2⟹ a₄₀ = 20⟹ 40th term of HP = 1/20∴ The 40th term of the required HP is 1/20.


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