Question

the 26th,11thand last termof ap are 0,3,-1/5 redpectively find comman diff and number of terms

Answer 1

We are given, a+25d = 0 ............................................(1)
                       a+10d = 3 .............................................(2)

By subtracting Eqn (1) From (2)

                    a + 10d = 3
                    a + 25d = 0
     
                So, -15d = 3
                           d = -1/5

By putting d = -1/5 in eqn (1)
            a + 10(-1/5) = 3
           a -2 = 3
           a = 5 
Now we have a = 5 and d = -1/5

Let there are n terms in AP then an = l = -1/5


             so, a + (n-1)d = -1/5
                   5 + (n-1)-1/5 = -1/5
                        (1-n)/5 = -1/5 - 5
                        (1-n)/5 = -26/5
                         (1-n) = -26
                   so, n = 27

So, Common Diff, d = 1/5 and No of terms = 27