If the sum of the first #100# terms of an arithmetic series with common difference #9# is #20888#, what is the first term?

1 Answer
Apr 10, 2017

Answer:

The first term is #-236.62#.

Explanation:

We use the formula #s_n = n/2(2a + (n - 1)d)# to find the sum of the first #n# terms of an arithmetic series with common difference #d# and first term #a#.

#20888 = 100/2(2a + (100 - 1)9)#

Solving for #a# we obtain:

#20888 = 50(2a + 891)#

#20888 = 100a + 44550#

#-23662 = 100a#

#a = -236.62#

#:.# The first term of the series is #-236.62#.

Hopefully this helps!