1.

The 11 th term and the 21 st term of an AP are 16 and 29 respectively then the 41 term of that AP

Answer»

Solution:-

Given

=> T₁₁ = 16

=>T₂₁ = 29

To find

=>T₄₁ =?

Formula

=> Tₙ = a + ( n - 1 )d

Now take

=> T₁₁ = 16

=> 16 = a + ( 11 - 1 )d

=> a + 10d = 16 .......(i)st eq

T₂₁ = 29

=> 29 = a + ( 21 - 1 )d

=> a + 20D = 29 .....(ii)ND eq

Now subtract (i)eq from (ii)eq

=> a + 20d - a - 10d = 29 - 16

=> 10d = 13 => d = 13/10

Now put the value of 10d on first equation

=> a + 10d = 16

=> a + 13 = 16

=> a = 3

Now we have to find T₄₁

=> T₄₁ = a + ( 41 - 1 )d

=> T₄₁ = 3 + 40 × 13/10

=> T₄₁ = 3 + 4 × 13

=> T₄₁ = 3 + 52

=> T₄₁ = 55



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