How do you find the sum of the arithmetic series 2 + 5 + 8 + ... + 56?

1 Answer
Mar 31, 2016

Answer:

#s_n= 551#

Explanation:

The sum of an arithmetic series is #s_n=n/2(a_1 +a_n)#
Where n is the number of terms
a_1 is the first term and
a_n is the last tern or the nth term

but in the given problem the nth term is not given , but we can determine its term by using the formula # a_n = a_1+ (n-1)d#
Where d is the common difference

Given : #2+5+8+...+56#
#a_n= 56 #
#a_1=2 #
#d=3#( just by substracring the second and the first term since we already know this is an arithmetic sequence, it has common difference)
#n=?#
By substituting to the equation
# 56 = 2+ (n-1)3#
#54=3n-3#
#57=3n#
#n=19#

So we already have the number of terms.
Now solving for the sum of the arithmetic sequence using the formula #s_n=n/2(a_1 +a_n)#

using the givens we have , substitute to the sum formula
#s_n=19/2(2+56)#
#s_n=19/2(58)#
#s_n=19(29)#
#s_n= 551#