Question

Find the 20 term of ap whose third term is 7 and 17 term exceeds tree time the third term by 2 also find its n th term

Answer 1

Answer:

T₂₀ = 26.4 and Tₙ = (25 + 8n) / 7

Step-by-step explanation:

Given 3rd term = 7

             T₃ = a + (3-1) d

              7 = a + 2d

             a + 2d = 7 ----------(1)

           Also, T₁₇ = 3T₃ + 2

                      a + 16d = 3(7) + 2

                     a + 16d = 21 + 2

                     a + 16d = 23------------(2)

solving (1) and (2),

                      d = 8/7

                     a = 33/7

                    T₂₀ = a + (n-1)d

                  T₂₀ = 33/7 + 19 (8/7)

                  T₂₀ = 185 / 7

                  T₂₀ = 26.4

                     Tₙ = a + (n-1)d

                     Tₙ = 33/7 + (n-1) (8/7)

                      Tₙ = (33 + 8n - 8) / 7

                     Tₙ = (25 + 8n) / 7