Answer:
See below.
Explanation:
For 3, we have:
1, 3, 6, ___, 15, 21, _____, 36, _______
Let's try to determine the pattern. From 1 to 3, we added 2.
From 3 to 6, we added 3.
So, it seems that the fourth term would be to add 4, and then add 5. Let's try it:
6+4=10
10+5=15.
So, it seems we're correct. So, we will add 6, then 7, and then 8, etc. Therefore, our correct sequence would be:
1 (+2), 3 (+3), 6 (+4), 10 (+5), 15 (+6), 21 (+7), 28 (+8), 36 (+9), 45
For 4, we have:
100, _____, 64, ______, 36, 25, _______
Notice that these all are perfect squares. 10 squared is 100, 8 squared is 64, etc. Thus, we can rewrite this as:
10², _____, 8², ______, 6², 5², ______
Therefore, our blanks would be:
10², 9², 8², 7², 6², 5², 4².
Evaluated, this woul be:
100, 81, 64, 49, 36, 25, 16.
And we're done!