Question

The fifth term in a sequence of numbers is 23. Each term is found by multiplying the previous term by 2 and adding 1. What is the third therm in this sequence?

Answer 1

Answer:  5

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Explanation:

• third term = x
• fourth term = 2(third term)+1 = 2x+1
• fifth term = 2(fourth term)+1 = 2(2x+1)+1 = 4x+2+1 = 4x+3

Set the fifth term equal to 23. Solve for x.

fifth term = 23

4x+3 = 23

4x = 23-3

4x = 20

x = 20/4

x = 5

The third term is 5. This leads to:

• fourth term = 2(third term) + 1 = 2*5+1 = 10+1 = 11
• fifth term = 2(fourth term)+1 = 2*11+1 = 22+1 = 23

We've confirmed the answer.

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Here's another way to get the answer:

The process "multiply previous term by 2, then add 1" can be reversed to: "subtract 1 from the previous term, then divide by 2". We undo each of the operations mentioned and we do so in reverse order.

So,

• fifth term = 23
• fourth term = (fifth term-1)/2 = (23-1)/2 = 22/2 = 11
• third term = (fourth term-1)/2 = (11-1)/2 = 10/2 = 5