Question

Question 11 Write the first five terms of the following sequence and obtain the corresponding series: a1 = 3, an = 3a(n-1) + 2 for all n>1

Class X1 - Maths -Sequences and Series Page 181

Answer 1

aₙ = 3aₙ_₁ + 2 where n>1
and a₁ = 3
so,
2nd term(a₂) = 3a₂_₁ + 2
a₂ = 3a₁ + 2
= 3 × 3 + 2
= 9 + 2
= 11


3rd term(a₃)= 3a₃_₁ + 2
a₃ = 3a₂ + 2
= 3 × 11 + 2
= 33 + 2
= 35

4th term(a₄) = 3a₄_₁ + 2
a₄ = 3a₃ + 2
= 3 × 35 + 2
= 105 + 2
= 107

5th term (a₅) =3a₅_₁ + 2
a₅ = 3a₄ + 2
= 3 × 107 + 2
= 321 + 2
= 323

6th term(a₆) = 3a₆_₁ + 2
a₆ = 3a₅ + 2
= 3 × 323 + 2
= 969 + 2
= 971

hence, first five term of this series are 11, 35, 107, 323, 971