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Current time:0:00Total duration:4:33

Video transcript

below our ordered pairs that represent the first six terms of two given patterns the first value in each pair is the term from pattern a and the second value is a term from pattern B in the answer box there are different statements about the two patterns choose all correct statements so let's think about what's going on here they said the first term is pattern a so pattern a the first so the first term in each of these coordinates is pattern a or in each pairs pattern a so pattern a goes from 1 to 2 to 4 to 8 to 16 to 32 so it looks like pattern a to go from the first term to the second term we multiplied by 2 we multiplied multiplied by 2 and then go from the second to the third term we also multiplied by 2 and we just keep we just keep multiplying by 2 multiplied by 2 and we just keep doing that 8 times 2 is 16 16 times 2 is 32 now let's think about what's going on with pattern B pattern B so pattern B is the second number in each of these in each of these pairs and it's just always 3 so there's a couple of ways to think about you could just say pattern B is always 3 you could say pattern B starts at 3 and we're just adding 0 every time or you could say that pattern B starts at 3 and we are multiplying by 1 every time either of those would give you would give you just three showing up over and over again over and over again so now that we've looked at these pairs which show the corresponding terms for pattern a and pattern B let's look at the choices here and see which of these apply in pattern a you can get from any term to the next by multiplying by a constant number well that looks right we go from the first term the second term by multiplying by 2 then we multiply by 2 again I go to the third term then we keep multiplying by 2 so that constant number that we're multiplying by to get to the next term is 2 so this looks right the next pair should be 52 comma 3 so let's think about this if we keep doubling for pattern a so this is going to be times 2 32 times 2 is 64 and then if we'd say that this is one times the previous term we're just going to get a three again so it should be 64 comma three should be the next one they say the next pair should be fifty two comma three so that's not right if we graph the pairs the points will be on the same line so let's think about that a little bit let's think about that so this is my vertical axis this is my horizontal axis on the horizontal axis I will graph pattern a and on my vertical axis I will graph pattern B pattern B and let's see pattern a pattern a goes all the way up to 32 so I'm going to try my best here so let's say that this is 32 then half of that is going to be 16 half of that is going to be 8 half of that is going to be for half of that it's going to be 2 and half of that is going to be 1 so these are all the points on pattern a but for any of them the corresponding term on pattern B is 3 so we have when pattern a is 1 pattern B is 3 1 3 when pattern a is 2 pattern B is 3 when pattern a is 4 pattern B is 3 when pattern a is 8 pattern B is 3 when pattern 8 is 16 pattern this is like a time when pattern a is 16 pattern B is 3 when pattern a is 32 pattern B is 3 and you see they all sit on a line they all sit on the line they all sit on this horizontal line at least the way that we've drawn it they all sit on this line that you probably can't see in yellow so let me do it in this red color they all sit on this line right over here so this looks right if we graph the pairs the points will be on the same line so I'll go with that one in pattern B you can get from any term to the next by multiplying by a constant number well yeah even though every term is the same term but you can get from a 3 to a 3 by always multiplying by 1 1 is a constant number so we're just multiplying every term by 1 so that also seems to be right so all of these are right except the second one the next pair isn't fifty two comma three it's going to be 64 comma three