Say what is the value of a?

Before going to the main question, let's find out the solution of two simple mathematical questions.
Suppose a simple question. If the number of two numbers is 85, then what is the sum of the two numbers? To find out the answer, first we get the producer of 85. Since the last digit of the number is 5, the number must be divisible by 5. If you divide 85 by 5, then answer 17. So we see, 85 = 5X17. Here are 5 and 17 two basic numbers. Since there is no other producer, so the number of two numbers is 85, their sum, (5 + 17) = 22

See another simple problem. We have solved such problems in the basins, such as (1 + 3 + 5 + ... + 99) = 2,500 The easiest way to find this is to first observe that it is a random element, in which the difference between each position is 1. The rule for finding the sum of this type is, sum = (first term + last term) x number / 2. We learned the formula in our childhood that we can still say the eyes closed completely. Now, since here the numbers begin with 1 in every step, ie 1, after 2, 3, ... and the last sentence 99, so we can easily find out that the number 50. To find it, do not count to 99 whole. Only five, five, five, seven, and nine, from these five verses, realize that since 1 to 9, the number of the sequence is 5, so in this 99, there will be 10 steps in the order of steps = 5x10 = 50. Now we can find out the sum using the formula. (1 + 99) X50 / 2 = 100x25 = 2,500

This week's puzzle
Say, (1 + 2 + 3 + ... + a) = 378 What is the value of a?