Question

The 8th term of an A.P. is -23 and its 12th term is -39. Then find the first and second terms of the A.P.

Answer 1

The 8th term of an Arithmetic Progression(AP) is t₈ = -23

The 12th term of an Arithmetic Progression(AP) is t₁₂ = -39

Let a be the first term and d be the common difference.

The general formula of nth term is t_n = a + (n-1)d

Equating the 8th and 12th term from general equation

8th term = t₈ = a + (8 - 1)d

-23 = a + 7d   ......(1)

12th term = t₁₂ = a + (12 - 1)d

-39 = a + 11d    .......(2)

Solving the equations (1) and (2)

(2) - (1) gives 

(a + 11d) - (a + 7d) = -39 - (-23)

(a + 11d) - (a + 7d) = -39 + 23

4d = -16

d = -16/4

d = -4

Putting the value of d in (1), we get

a + 7 x (-4) = -23

a - 28 = -23

a = -23 + 28

a = 5

So, the first term of A.P. is 5.

The general formula of nth term is t_n = a + (n - 1)d

Second term = 5 + (2 - 1) x (-4)

= 5 - 4

= 1

Therefore, First and Second terms of A.P. is 5 and 1.