Complete Group C: Unravel the Sequence Pattern

Question

A sequence represents the division of boys and girls into groups and is structured according to a term-to-term rule.

Complete group C.

groupBoysGirlsABCDEF5917212559132125

Video Solution

Solution Steps

00:08 Let's complete group C together.
00:12 First, find the difference between all the girls' groups.
00:22 Next, calculate the difference from group B to group C.
00:27 This will give us the number of girls in group C.
00:35 Now, use the same steps to figure out how many boys are in group C.
00:41 Find the difference between all the boys' groups.
00:46 Then, calculate the difference from group B to group C.
00:51 This is the number of boys in group C.
00:55 And that's how we solve the problem! Great job!

Step-by-Step Solution

To solve this problem, we need to recognize the patterns for both boys and girls across the groups:

  • For the boys: The sequence given is 5, 9, 17, 21, 25 for groups A, B, D, E, F respectively. Observing the differences: 95=4 9 - 5 = 4 , 179=8 17 - 9 = 8 , 2117=4 21 - 17 = 4 , 2521=4 25 - 21 = 4 . This means the sequence is increasing by alternating values of 4 and 8. Thus, the missing number for group C (after 9) should be 9+8=17 9 + 8 = 17 .
  • For the girls: The sequence given is 25, 21, 13, 9, 5. Observing the differences: 2125=4 21 - 25 = -4 , 1321=8 13 - 21 = -8 , 913=4 9 - 13 = -4 , 59=4 5 - 9 = -4 . This means the sequence is decreasing by alternating values of -4 and -8. Thus, the missing number for group C (after 21) should be 218=13 21 - 8 = 13 .

Therefore, the values for group C are:

13, 17

Answer

13, 17