Find the sum of arithmetic series 5,11,17,,599?

29705

Step-by-step explanation:

It is clear that this answer increase in increments of 6, as 11-5 =6, and the same is true for 17 - 11. A simplistic solution to this sequence comes in the form of:

6x +5 = 599

where x is equivalent to the total number of terms in between.

6x = 594, x = 99.

Knowing the value of x, the sum of this sequence can be found as each successive term is simply a+6 which iterates for 99 times, where a is the previous value.

Let's try to find an equation to represent the total value of this series with the first 3 values of 5, 11, 17.

5, 5+6, 5+6+6

As you can see, each iteration matches the number of values it adds to the equation.

As you know this fact, your answer can be found using the counting method (1+2+3+4+5+6+7+ +n(in this case it is 99))x 6 +5 to find your value. Of course, it is unrealistic to add all of these numbers up one by one, so take the midpoint of this set (99/2) which is 49.5. Consecutive adding is a long process and would be easier explained if you looked it up yourself. In this scenario, remove 99 from the set and start with 98. 98+1 = 99, 97+2=99, 96+3 = 99. As you can see, if you take the first value and the last value and add then together, it gives 99, regardless of which value you are currently on. There are 49 of such pairs, so to find the total of 1+2+3+4+5 + --- +99 do:

(99x49)+99 = 4950.

Multiply this value by 6 = 29700

Add 5 to the end, and you have your answer 29705.