Question

What is the fifth term of the recursive formula a(n)=2a(n-1)-1 with the first term of 3? A. 7 B. 17 C. 33 D. 65

Answer 1

To find the fifth term of the recursive sequence a(n)=2a(n-1)-1 with a(1)=3, we calculate each term sequentially and find that the fifth term is 33.

Step-by-step explanation:

The question is asking for the fifth term of the recursive formula a(n) = 2a(n-1) - 1 with the first term being 3. To find the fifth term, we calculate each term step by step, starting with the given first term.

First term, a(1) = 3 (given)

Second term, a(2) = 2×3 - 1 = 5

Third term, a(3) = 2×5 - 1 = 9

Fourth term, a(4) = 2×9 - 1 = 17

Fifth term, a(5) = 2×17 - 1 = 33

Therefore, the fifth term of the sequence is 33.

Answer 2

`\bf \begin{array}{ccll} n&term&value\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 1&a(1)&3\\ 2&a(2)&2a(2-1)-1\\ &&2a(1)-1\\ &&2(3)-1\\ &&5\\ 3&a(3)&2a(3-1)-1\\ &&2a(2)-1\\ &&2(5)-1\\ &&9\\ 4&a(4)&2a(4-1)-1\\ &&2a(3)-1\\ &&2(9)-1\\ &&17\\ 5&a(5)&2a(5-1)-1\\ &&2a(4)-1\\ &&2(17)-1\\ &&33 \end{array}`