Question

The sum of a number and its reciprocal is 3 41/80 .Find the number .

Answer 1

$T_{n}$ = a + (n-1)d

Here, first term a = 3
          common difference d = 5
Therefore, $T_{n}$ = 3 + (n-1)5
             or,                   273 = 3 + 5n - 5
             or,                   275 = 5n
             or,                       n = 55

Therefore, we can conclude that there are 55 terms in the A.P.

Therefore, $20^{th}$ term from last = $(55-20)^{th}$ term                                                                             from beginning
                                                                     = $35^{th}$ term.

Therefore, $T _{35}$ = 3 + (35-1)5
                                              = 3 + 170
                                              = 173