Question

If the 5th and 12 th term of an Ap is 14 and 35 respectively find 1 st term and common difference also find 20 th term

Answer 1

Solution:-

Given:-

=> T₅ = 14

=> T₁₂ = 35

To find

=>First term ( a ), Common difference ( d ) and T₂₀

Formula

=> Tₙ = a + ( n - 1 )d

Now take:- T₅

=> 14 = a + ( 5 - 1 )d

=> 14 = a + 4d

=> a + 4d = 14 ......(i)eq

Now take :- T₁₂

=> 35 = a + ( 12 - 1 )d

=> 35 = a + 11d

=> a + 11d = 35 ......(ii) eq

Now Subtract (ii)eq from (i)eq

=> a + 4d - a - 11d = 14 - 35

=> - 7d = -21

=> d = 21/7

=> d = 3

Now put the value of d = 3 on (ii)eq

=> a + 11d = 35

=> a + 11 × 3 = 35

=> a + 33 = 35

=> a = 35 - 33

=> a = 2

So first term ( a ) = 2 , common difference ( d ) = 3

Now find T₂₀

=> T₂₀ = a + ( n - 1 ) d

=> T₂₀ = 2 +( 20-1)× 3

=> T₂₀ = 2 + 19 × 3

=> T₂₀ = 57 + 2

=> T₂₀ = 59

Answer 2

Solution is given in the above attachment..