If in an A.P., T₇ = 18, T₁₈ = 7, find T₁₀₁.

Formula Used.

a_n = a + (n–1)d

a₇ = a + (7–1)d

a₇ = a + 6d

If 7^th term of A.P is given as 18

Then,

a + 6d = 18

we get a = 18–6d ......eq 1

a₁₈ = a + (18–1)d

a₁₈ = a + 17d

If 18^th term of A.P is given as 7

Then,

a + 17d = 7

we get a = 7–17d ......eq 2

Equating both eq 1 and eq 2

We get ;

18–6d = 7–17d

17d–6d = 7–18

11d = –11

d = = –1

Putting d in eq 1 we get ;

a = 18–6×(–1)

= 18 + 6 = 24

For 101^st term

a_n = a + (n–1)d

a₁₀₁ = 24 + (101–1)(–1)

= 24–100

= –76