Matthew Fan's answer to lim's Junior College 2 H3 Maths Singapore question.
Alternative working without actually writing it as a sum of the terms or subtracting equations :
Sn - kS(n-1) = c
Based in question's instructions,
S(n-1) - kS(n-2) = c
So Sn - kS(n-1) = S(n-1) - kS(n-2)
Sn - S(n-1) = k( S(n-1) - S(n-2) )
un = k u(n-1)
un / u(n-1) = k
Common ratio k so it's a G.P
Sn - kS(n-1) = c
Based in question's instructions,
S(n-1) - kS(n-2) = c
So Sn - kS(n-1) = S(n-1) - kS(n-2)
Sn - S(n-1) = k( S(n-1) - S(n-2) )
un = k u(n-1)
un / u(n-1) = k
Common ratio k so it's a G.P
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