Question

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

Answer 1

`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`