Given :
The sequence is given as : 3, 6, 12, 24, 48, 96,...
To Find :
A formula to represent the nth term of the given sequence.
Solution :
Breaking down each term we get :
3 = 3 × 2⁰ 1 - term
6 = 3 × 2¹ 2 - term
12 = 3 × 2² 3 - term
24 = 3 × 2³ 4 - term
48 = 3 × 2⁴ 5 - term
From above observation we can say that n th term is given by 3 × 2ⁿ⁻¹ .
Therefore, the nth them of the sequence is given by ( 3 × 2ⁿ⁻¹ ) .