X Y 1 3 2 7 10 39

Asked By Claudia On 03/13/2017 22:12

Answers

This is a sequence. My first term is 3. My second term is 7. My tenth term is 39. Think of a function machine. We need to figure out what happens to our terms when we drop them into the function machine. Since my first term is 3, this means that I dropped in a 1 and the machine spit out a 3. Since my second term is 7, this means that I dropped in a 2 and the machine spit out a 7. For my tenth term of 39, this means that I dropped in a 10 and the machine spit out a 39. What happened? Try different operations. For example, one possibility for 1, 3 is that I dropped in a 1; and the machine multiplied my number by 3 and spit out a 3. Does this rule work for the second term in my sequence? If I drop in a 2, and the machine multiplies my number by 3, will it spit out a 7? No, it spit out a 6. So my rule is NOT multiply by 3, so we try a different rule. What if we multiply by 4? If I drop in a 1 and the machine multiplies by 4, it would spit out a 4; but I need it to spit out a 3. Well, 4 - 1 would give me 3; so maybe my rule is multiply by 4 and then subtract 1. Let's try for the second term. I drop in a 2. The machine multiplies by 4, which gives me 8 and then subtracts 1, which gives me 7. It works! Let's try for the tenth term. I drop in a 10. The machine multiplies by 4, which gives me 40 and then subtracts 1, which gives me 39. It works! I have my rule! Multiply the input by 4 and subtract 1 to get the output. y = 4x - 1 or f(x) = 4x - 1
Answered On 03/21/2017 14:03