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

1 Answer
Mar 31, 2016

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