What is the 21sr term in arithmetic sequence in which

Question

a₃ is 59 and a₇ is 103

enter only the term

Answer 1

Let a_n = nth term of an arithmetic sequence

            = a₁ + (n-1)d, where a₁ = first term and d = common                                                                                                            difference

 

a₃ = a₁ + 2d = 59

a₇ = a₁ + 6d = 103

 

Subtract the equations to get -4d = -44.  So, d = 11

 

a₁ + 2d = a₁ + 22 = 59

 

                          a₁ = 37

 

Therefore, a_n = a₁ + (n-1)d

                    a₂₁ = 37 + (20)(11)

                           = 37 + 220 = 257