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How do you find the sum of the arithmetic sequence given 8, 3, -2, -7, -12, ....., -57?

1 Answer
Jul 9, 2016

Step 1: Find the number of terms

The nth term of an arithmetic sequence is given by #t_n = a + (n - 1)d#. We know #t_n# (-57), r (-5) and a (8), however we don't know n. We will therefore solve for #n#.

#-57 = 8 + (n- 1)-5#

#-57 = 8 - 5n + 5#

#-57 - 13 = -5n#

#-70 = -5n#

#n = 14#

#:.# The sequence has #14 # terms.

Step 2: Apply the formula for sum:

When dealing with arithmetic series, we will frequently use two formulas to help us find the sum. They are:

#s_n = n/2(2a + (n - 1)d)#

#s_n = n/2(a + t_n)#

Since we know the first term, the last term and the number of terms, we have enough information to use the latter; this one is more efficient and easy to use than the first.

#s_n = n/2(a + t_n)#

#s_14 = 14/2(8 + (-57))#

#s_14 = 7(8 - 57)#

#s_14 = -343#

Hence, the sum of this arithmetic sequence is #-343#.

Practice exercises:

  1. Determine the sum of the following sequence:

#3, 14, 25, ..., 179#

Hopefully this helps, and good luck!