Can you find a recursive rule for the formula tn = 3 × 10n-1 that generates the geometric progression Class 9

Can you find a recursive rule for the formula t_n = 3 × 10^n-1 that generates the geometric progression Class 9

Question 1.

Can you find a recursive rule for the formula t_n = 3 × 10^n-1 that generates the geometric progression 3, 30, 300, 3000,... ? Class 9

Answer:

Given:

t_n = 3 × 10^n-1

The sequence is: 3, 30, 300, 3000,...

Since each term is obtained by multiplying the previous term by 10.

So the recursive rule is: t₁ = 3 and

t_n = 10t_n-1, n ≥ 2

i.e., t₂ = 10t₁ = 30

t₃ = 10t₂ = 300

t₄ = 10t₃ = 3000.