Question

Write the first 5 terms of each A.P.

a) 4th term is 2, 7th term is 3

b) 3rd term is 2 5th term is 3.

Answer 1

(a) a₄ = 2, a₇ = 3

⇒ a + 3d = 2

a + 6d = 3

⇒ 3d = 1

⇒ d = 1/3

\(\therefore\) a + 1 = 2

⇒ a = 1

\(\therefore\) a₁ = a = 1

a₂ = a + d = 1 + 1/3 = 4/3

a₃ = a + 2d = 1 + 2/3 = 5/3

a₄ = a + 3d = 1 + 1 = 2

a₅ = a + 4d = 1 + 4/3 = 7/3

(b) a₃ = 2, a₅ = 3

⇒ a + 2d = 2

⇒ a + 4d  = 3

\(\therefore\) 2d = 1 ⇒ d = 1/2

\(\therefore\)  a + 1 = 2 ⇒ a =1

\(\therefore\) a₁ = a = 1

a₂ = a + 2d = 1 + 1 = 2

a₄ = a + 3d = 1 + 3/2 = 5/2

a₅ = a + 4d = 1 + 2 = 3