Find A.P. if Tn, Tm are as given below:

T₇ = 12, T₁₂ = 72

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 12

Then,

a + 6d = 12

we get a = 12–6d ......eq 1

a₁₂ = a + (12–1)d

a₁₂ = a + 11d

If 12^th term of A.P is given as 72

Then,

a + 11d = 72

we get a = 72–11d ......eq 2

Equating both eq 1 and eq 2

We get ;

12–6d = 72–11d

11d–6d = 72–12

5d = 60

d = = 12

Putting d in eq 1 we get ;

a = 12–6×12

= 12–72 = –60

As a = –60 and d = 12

Then;

a₁ = a + (n–1)d = –60 + (1–1)(12) = –60

a₂ = a + (n–1)d = –60 + (2–1)(12) = –60 + (12)×1 = –48

a₃ = a + (n–1)d = –60 + (3–1)(12) = –60 + (12)×2 = –36

a₄ = a + (n–1)d = –60 + (4–1)(12) = –60 + (12)×3 = –24

a_n = a + (n–1)d = –60 + (n–1)(12) = 12n – 72

∴ The A.P is –60, –48, –36, –24……, 12n – 72