Q. 4 A4.5( 2 Votes )

# Find A.P. if Tn,

Formula Used.

an = a + (n–1)d

a7 = a + (7–1)d

a7 = a + 6d

If 7th 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 12th 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

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

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

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