(8) The 10th and 18th terms of an A.P are 41 and 73 respectively. Find the 27th term

Solution:

10th term = 41

18th term = 73

a + 9 d = 41   ------- (1)

a + 17 d = 73   ------- (2)

Subtracting the second equation from first equation

                                      a + 9 d = 41

                                      a + 17 d = 73

                                    (-) (-) (-)

                                   -------------------

                                          -8 d = -32

                                              d = (-32)/(-8)

                                              d = 4

Substitute d = 4 in the first equation

                   a + 9 (4) = 41

                   a + 36 = 41

                          a = 41 – 36

                         a = 5

Now we have to find 27th term          

tn =  a + (n - 1) d

    = 5 + (27-1) 4

    = 5 + 26 (4)

   = 5 + 104

   = 109