What is the sum of the arithmetic series 2 + 5 + 8 + ... + 53?

1 Answer
Feb 21, 2016

Answer:

First, we must find the number of terms, n.

Explanation:

#t_n = a + (n - 1)d#

#53 = 2 + (n - 1)3#

#53 = 2 + 3n - 3#

#54 = 3n#

#18 = n#

Now that we know the number of terms we can use the formula #s_n = n/2(t_1 + t_n)#

#s_18 = 18/2(2 + 53)#

#s_18= 9(55)#

#s_18 = 495#

The sum is of 495.

When finding the sum of an arithmetic series, there are two formulas that you may use: the one presented above and #s_n = n/2{2a + (n - 1)d}#. You use the latter when you don't know the last term.

Practice exercises:

  1. Find the sum of the following series: #5, 11, 17, ..., 131#

  2. Find the sum of a series with the following characteristics.

  3. First three terms: #7, -1, -9, ...#

  4. #n = 33#

Hopefully this helps!