A finite sequence such as

in which each succeeding term is obtained by adding a fixed number to the preceding term is called an arithmetic progression. The general form of an arithmetic progression with n terms is therefore
 

where a is the first term and d is the fixed difference between successive terms.

In the arithmetic progression above, the first term is 2 and the common difference is 3. The second term is  the third term is  the fourth is  and the nth is 2 + 3(n - 1). Since  or 101 = 2 + 3(34 - 1), one has to add 3 thirty-three times to obtain the nth term. This shows that there are thirty-four terms here. The sum S of these thirty-four terms may be found by the following technique. We write the sum with the terms in the above order and also in reverse order, and add:

Hence S = 3502/2 = 1751.
 

Sunday, March 15, 1998