The number pattern increases by consecutive even numbers. By continuing this pattern, the next two terms after 34 are determined to be 46 and 60.
The student is asking about a consistent number pattern and wants to determine the next two terms of the sequence: 6, 10, 16, 24, 34,.... To identify the pattern, let's examine the differences between consecutive numbers: 10-6=4, 16-10=6, 24-16=8, 34-24=10. We see that the difference itself is increasing by 2 each time. Therefore, to find the next difference after 10, we add 2 to get 12. Now add this difference to the last term (34+12=46). For the following term, increase the difference by another 2 (12+2=14) and add it to 46 (46+14=60).
To conclude, the next two terms in the pattern are 46 and 60.