Write the first six terms of the sequences given by (i) a1 = a2 = 1 =

1.	Write the first six terms of the sequences given by (i) a1 = a2 = 1 = an - 1 + an - 2 (n ≥ 3)(ii) a1 = 4, an + 1 = 2nan
Answer» (i) Here a₁ = a₂ = 1 = a_{n - 1} + a_{n - 2} (n ≥ 3) Putting n = 3, a₃ = a₂ + a₁ = 1 + 1 = 2 Putting n = 4, a₄ = a₃ + a₂ = 2 + 1 = 3 Putting n = 5, a₅ = a₄ + a₂ = 3 + 2 = 5 Putting n = 6, a₆ = a₅ + a₄ = 5 + 3 = 8 ∴ First six terms of the sequence are 1, 1, 2, 3, 5, 8 (ii) Here a₁ = 4 and a_{n + 1} = 2na_n Putting n = 1, a₂ = 2 × 1 × a₁ = 2 × 1 × 4 = 8 Putting n = 2, a₃ = 2 × 2 × a₂ = 4 × 8 = 32 Putting n = 3, a₄ = 8 × 192 = 1536 Putting n = 4, a₅ = 2 × 4 × a₄ = 8 × 192 = 1536 Putting n = 5, a₆ = 2 × 5 × a₅ = 10 × 1536 = 15360

Write the first six terms of the sequences given by (i) a1 = a2 = 1 = an - 1 + an - 2 (n ≥ 3)(ii) a1 = 4, an + 1 = 2nan

Answer»

(i) Here a₁ = a₂ = 1 = a_{n - 1} + a_{n - 2} (n ≥ 3)

Putting n = 3, a₃ = a₂ + a₁ = 1 + 1 = 2

Putting n = 4, a₄ = a₃ + a₂ = 2 + 1 = 3

Putting n = 5, a₅ = a₄ + a₂ = 3 + 2 = 5

Putting n = 6, a₆ = a₅ + a₄ = 5 + 3 = 8

∴ First six terms of the sequence are 1, 1, 2, 3, 5, 8

(ii) Here a₁ = 4 and a_{n + 1} = 2na_n

Putting n = 1, a₂ = 2 × 1 × a₁ = 2 × 1 × 4 = 8

Putting n = 2, a₃ = 2 × 2 × a₂ = 4 × 8 = 32

Putting n = 3, a₄ = 8 × 192 = 1536

Putting n = 4, a₅ = 2 × 4 × a₄ = 8 × 192 = 1536

Putting n = 5, a₆ = 2 × 5 × a₅ = 10 × 1536 = 15360