we are trying to find the expression to solve for the nth term in the pattern 3, 6, 10, 15, 21 can you help us? Hi Patrick,
The first thing to do is to look at the differences between successive terms. 10  6 = 4 15  10 = 5 21  15 = 6 28 + 8 = 36 36 + 9 = 45
From the pattern above the sequence can be written t_{2} = 3 + [3] t_{3} = 3 + [3 + 4] t_{4} = 3 + [3 + 4 + 5] . . . t_{n} = 3 + [3 + 4 + 5 + ... + (n+1)] The expression in the square brackets above you can find using the method of Gauss. (There is an easier allpication of this method in an earlier problem.)
There are n  1 terms in the expression in square brackets so write it as Adding these two expressions (add down) gives
Hence and thus Denis
