Consider the arithmetic sequence

Other · Subjective · ISC · Mathematics · Algebra · Arithmetic progressions

Problem

u_1, u_2, u_3, \dots

. The sum of the first

n

terms of this sequence is given by

S_n = n^2 + 4n

. (a.i) Find the sum of the first five terms. (a.ii) Given that

S_6 = 60

, find

u_6

. (b) Find

u_1

. (c) Hence or otherwise, write an expression for

u_n

in terms of

n

. Consider a geometric sequence,

v_n

, where

v_2 = u_1

and

v_4 = u_6

. (d) Find the possible values of the common ratio,

r

. (e) Given that

v_{99} < 0

, find

v_5