Question

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

Answer 1

The general term of an A.P. is given by

t_n = a + (n – 1)d

Now, t₅ = 6

`=>` a + (5 – 1)d = 6

`=>` a + 4d = 6  ...(i)

And t₆ = 5

`=>` a + (6 – 1)d = 5

`=>` a + 5d = 5  ...(ii)

Subtracting (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)

`=>` t₁₁ = 10 + (11 – 1)(–1)

= 10 – 10

= 0