A sequence represents the division of boys and girls into groups and is structured according to a term-to-term rule.
Complete group C.
Video Solution
Solution Steps
00:08Let's complete group C together.
00:12First, find the difference between all the girls' groups.
00:22Next, calculate the difference from group B to group C.
00:27This will give us the number of girls in group C.
00:35Now, use the same steps to figure out how many boys are in group C.
00:41Find the difference between all the boys' groups.
00:46Then, calculate the difference from group B to group C.
00:51This is the number of boys in group C.
00:55And 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: 9−5=4, 17−9=8, 21−17=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.
For the girls: The sequence given is 25, 21, 13, 9, 5. Observing the differences: 21−25=−4, 13−21=−8, 9−13=−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 21−8=13.