A sequence is given by the recursive rule t₁ = 2, tₙ₊₁ = 3tₙ - 2 for n ≥ 1. Which term of the sequence is 730?

A sequence is given by the recursive rule t₁ = 2, tₙ₊₁ = 3tₙ - 2 for… — Mathematics Part 1 · Predicting What Comes Next: Exploring Sequences and Progressions

Question 33 of 51advanced🔧 ApplyNumerical4 marks

A sequence is given by the recursive rule $t_1 = 2$ , $t_{n+1} = 3t_n - 2$ for $n \geq 1$ . Which term of the sequence is 730?

Correct Answer

7th term

Exercise: Exercise Set 8.3 | Q: 3 | (Page 20)

For More Understanding

Explanation

Following the method shown in the context for recursive sequences, we successively substitute the values of n to compute each term until we reach the value 730.

Solution Steps

Step 1: Given $t_1 = 2$ .
Step 2: Calculate $t_2 = 3t_1 - 2 = 3(2) - 2 = 4$ .
Step 3: Calculate $t_3 = 3t_2 - 2 = 3(4) - 2 = 10$ .
Step 4: Calculate $t_4 = 3t_3 - 2 = 3(10) - 2 = 28$ .
Step 5: Calculate $t_5 = 3t_4 - 2 = 3(28) - 2 = 82$ .
Step 6: Calculate $t_6 = 3t_5 - 2 = 3(82) - 2 = 244$ .
Step 7: Calculate $t_7 = 3t_6 - 2 = 3(244) - 2 = 730$ . Thus, 730 is the 7th term of the sequence.

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