Find the sum of the Arithmetic Series upto 36 terms 2, 5, 8, 11,...

Arithmetic Series ::

An Arithmetic Series is a series of numbers in which each term increases by a constant amount.

How to find the sum of the Arithmetic Sequence or Series for the given Series ::

When the series contains a large amount of numbers, its impractical to add manually. You can quickly find the sum of any arithmetic sequence by multiplying the average of the first and last term by the number of terms in the sequence.

That is given by  S n = n ( a 1 + a n ) 2 Where n = number of terms, a1 = first term, an = last term

Here Last term is given by  a n = a 1 + n - 1 d where d = common difference

Now given Arithmetic Series is 

2, 5, 8, 11,...

Here a1 = 2,  d = 3, n = 36 

Now,  $$\begin{gathered} a n = a 1 + n - 1 d \\ a 36 = 2 + 36 - 1 3 = 105 + 2 = 107 \end{gathered}$$

Now, Sum to 36 terms is given by

S 36 = 36 ( 2 + 107 ) 2 = 36 x 109 2 = 3924 2 = 1962

Therefore, Sum to 36 terms of the series 2, 5, 8, 11,... is 1962.