The nth term of a sequence is given by the expression (2n+3)^2.find the (a) first four terms (b)the 8th term and(c)The difference between the 9th and 10th term.
plug and chug
n = 1 --> (2+3)^2 = 25
n = 2 --> (4+3)^2 = 49
etc
by the way (2n+3)^2 = 4 n^2 + 12 n + 9
which is easy too
a(9) = (21)^2
a(10) = (23)^2
so 529-441 = 88
or for fun
(2[n+1]+3)^2 - [4 n^2 + 12 n + 9]
(2n+5)^2 - 4 n^2 - 12 n - 9
4n^2 + 20 n + 25 - 4 n^2 - 12 n - 9
8 n + 16
8(9) + 16 = 88 remarkable :)