Question 1143233
<br>
The n-th term is the difference between the sum of the first n terms and the sum of the first (n-1) terms:<br>
{{{t(n) = (2n-n^2)-(2(n-1)-(n-1)^2) = (2n-n^2)-(2n-2-n^2+2n-1) = -2n+3}}}<br>
So the first term is -2(1)+3 =1 and the common difference is -2.<br>
ANSWERS:
(a) the first term is 1
(b) since the sequence is arithmetic, the sum of the last three terms (terms 13, 14, and 15) is 3 times the 14th term:
{{{3(-2(14)+3) = 3(-28+3) = 3(-25) = -75}}}