Bank savings, solution 1º) C0 = 5,000 $ ;
(
C 1=5,000× 1+
)
2.5 +1,000=6,125 $ 100
(
2º) C n +1= 1+
;
(
C 2=6,125× 1+
)
2.5 +1,000=7,278.125 $ 100
)
2.5 C +1,000=1.025C n +1,000 . 100 n
This sequence is neither arithmetic, nor geometric, because from one term to the next, we not only multiply by 1.025, but we also add 1,000 $. 3º) t n =C n +40,000 . a) To prove that the sequence (tn) is geometric, we calculate
t n+1 tn
and we try to prove that it is a constant. t n+1 C n+1 +40,000 1.025C n +1,000+40,000 1.025 C n +41,000 1.025(C n +40,000) = = = = =1.025 tn C n +40,000 C n+40,000 C n +40,000 (C n +40,000)
therefore the sequence (tn) is geometric and its ratio is 1. 025. b) t n =t 0 ×q n =(5,000+40,000)×1.025n=45,000×1.025n . C n =t n −40,000=45,000×1.025n−40,000 On the 1 st of january 2021, C 10=45,000×1.02510 −40,000≈17,603.80 $ .
