Take any three consecutive even numbers and add them , say ,
` 2+4 + 6= 12 , 4 +6 , 8 = 18 , 6 + 8 + 10 = 24 , 8 + 10 + 12 = 30` and so on.
Is there any pattern can you guess in these sums? What can you conjecture about them?

If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8 } and D = { 7, 8, 9, 10 } , find A ∪ B ∪ C

If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8 } and D = { 7, 8, 9, 10 } , find A ∪ B ∪ D

If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8 } and D = { 7, 8, 9, 10 } , find B ∪ C ∪ D

If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8 } and D = { 7, 8, 9, 10 } , find A ∪ C

If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8 } and D = { 7, 8, 9, 10 } , find B ∪ C

If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8 } and D = { 7, 8, 9, 10 } , find A ∪ B

If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8 } and D = { 7, 8, 9, 10 } , find B ∪ D

Let A = { 2, 4, 6, 8} and B = { 6, 8, 10, 12} . Find A ∪ B .

Distance between the two planes : 2x + 3y + 4z = 4 and 4x + 6y + 8z = 12 is

The following geometric arrays suggest a sequence of numbers. (a) Find the next three terms . (b) Find the 100^(th) term . (c) Find the n^(th) term . The dots here arranged in such a way that they form a rectangle. Here T_1 =2 , T_2 = 6 , T_3 = 12 , T_4 = 20 and so on. Cay you guess what T_5 is ? What about T_6 ? What about T_n ? Make a conjecture about T_n .