Provided for clarification (hopefully):

I understood this challenge to be asking: For a series of integers not less than 1 and through n (1..n), square the integer (i*i), add one (+1), and add to the sum (+ sum; the sum beginning at 0).

So above, the series is 1 through n. Starting at a base of 0 (the beginning sum) you perform the operation {sum + (i^2 + 1)}.

The inject/reduce method keeps track of the sum and returns the final sum at the end.

Solution:

def sum_terms(n)
  # your code here
    (1..n).inject(0) {|sum, i| sum + (i*i + 1) }
end

(1..n) # series of integers

.inject(0) # inject/reduce method with base 0

{|sum, i| # elements to be used in operation

sum + (i*i + 1) } # operation