Question

Let {un). n € Z", be an arithmetic sequence with first term equal to a and common difference of d,
where d *0. Let another sequence (vn), ne zt, be defined by v, = 2"
(a) (i) Show that
+1
is a constant
1
(ii) Write down the first term of the sequence {Un}
(iii) Write down a formula for V, in terms of a, d and n.
(4)
(b) Let S, be the sum of the first n terms of the sequence {n},
(1) Find S. in terms of a, d and n.
(ii) Find the values of d for which
Vi exists.
(8)
You are now told that
does exist and is denoted by S.
(111) Write down S in terms of a and d.
(iv) Given that S = 29+1 find the value of d.
(c) Let (w.), n e Z*. be a geometric sequence with first term equal top and common ratio q. where p
(6
and q are both greater than zero. Let another sequence (2n} be defined by Zn = Inw,
Find
21 giving your answer in the form Ink with k in terms of n, p, and q.
[Total 18 marks)
#70

Answer 1

Answer:

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