The nth term, un, of a geometric sequence is given by un = 3 (4)^n +1, n ∈ Z^+.
(a) Find the common ratio r.
(b) Hence, or otherwise, Find Sn, the sum of the first n terms of this sequence.
the ratio must be
(3*4^(n+1) + 1) / (3*4^n + 1)
But since that depends on n, you must have a typo
Sn = 4^(n+1) + n - 4
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