The sum of the first n terms of a sequence is n^2 + 5n. What is the 1000th term of the sequence?
The list of numbers is just even numbers starting at 6, so the 1000th term would be 2006.
The sequence is:
3, 6, 9, 12, 15, 18, 21 =n^2 + 5*n=7^2 + 35=84
Therefore the 1000th term =First term + 3*(1000 - 1)
=3 + (3*999)
=3 + 2,997
=3,000 - which is 1000th term.
The sum of the first term is just the first term. So if we plug in 1 to the equation, we'll find the first term which is (1^2) + 5 * 1 = 6. From this I can already see the difference in our solutions.