Question

The sum of the first n terms of a sequence is given by Sn = n^2-2n.
a. Find the first, third and sixth term.
b. Find an expression for the nth term.

Answer 1

a. To find the first term, just plug 1 into the equation for the value of n.
\[\large S _{1}=1^{2}-(2\times1)=you\ can\ calculate\]

Answer 2

Lets call the first term t1. We know that t1 must equal S1. If we find the sum of the first two terms, S2, and subtract the first term we will have the value of the second term.
\[\large t _{2}=S _{2}-S _{1}=(2^{2}-(2\times2))-(1^{2}-(2\times1))\]
Next we can find the sum of the first 3 terms and subtract the sum of the first two terms to find the third term.

Answer 3

The sixth term can be found by subtracting the sum of the first 5 terms from the sum of the first 6 terms:
\[\large t _{6}=S _{6}-S _{5}=(6^{2}-12)-(5^{2}-10)\]

Answer 4

Thank you :)

Answer 5

You're welcome :)