Question

If 5th and 6th terms of an A.P are respectively 6 and 5. Find the 11th term of the A.P

Answer 1

The general term of an A.P is given by

`t_n = a + (n - 1)d`

Now `t_5 = 6`

=> a + (5 - 1)d = 6

=> a + 4d = 6 ....(i)

And `t_6 = 5`

=> a + (6 - 1)d = 5

=> a + 5d = 5 ...(ii)

Substracting (ii) from (i) we get

-d = 1

=> d = -1

Substituting d = -1 in (i) we get

a + 4(-1) = 6

=> a - 4 = 6

=> a = 10

`=> t_n = 10 + (n - 1)(-1)`

`=> t_11 = 10 + (11 - 1)(-1) = 10 - 10 = 0`