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Verified answer
U1 + U2 = 45a + ar = 45
a( 1 + r) = 45
(1 + r) = 45/a
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U3 + U4 = 20
ar² + ar³ = 20
ar²(1 + r) = 20
ar² (45/a) = 20
45r² = 20
r² = 20/45
r² = 4/9
r = √ (4/9)
r =2/3 (+)
1 + 2/3 = 45/a
5/3 = 45/a
(3)(45) = 5a
a = (3)(45)/5
a = 27
S∞ = a/(1-r)
S∞ = 27 / (1-2/3)
S∞ = 27/(1/3)
S∞ = 27 × 3/1
S∞ = 81
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