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Sequences and Series: Fred
Transcript of Sequences and Series: Fred
plan to lose 182 pounds over a year. -182=224 Fred's plan calls for a loss of 3.5 pounds every week for a year. 406, 402.5, 399, 395.5, 392,...,224 Common Difference: Recursive Formula: 1 = a -3.5 n-1 = 406 a n Explicit Formula: a = 406+(n-1)(-3.5) n 52 k=1 406+(n-1)(-3.5) Fred also wants to make money. He developes a plan to accumulate money over time. By depositing $100 in the bank, Fred
agreed on a deal that will increase
his deposit by 8% every month for
5 years. 100, 108, 116.64, 125.97, 136.05, ..., 10125.71 a = a (1.08) n n-1 Explicit Formula: a = 100(1.08) n n -3.5 a Sequence: Series: Recursive Formula: 60 k=1 100(1.08) n Fred's wife wants to celebrate significant moments in
Fred's weight loss journey and needs to create a schedule. a) How many pounds will Fred lose after 15 weeks? a = 406+(15-1)(-3.5) 15 = 406+(14)(-3.5) = 406-49 = 357 Answer:
Fred will lose 49 pounds after 15 weeks. b) When will Fred weigh less than 300 pounds? 300 = 406+(n-1)(-3.5) 300-406 = (n-1)(-3.5) -106 = -3.5n + 3.5 -106 - 3.5 = -3.5n -109.5 = -3.5n -109.5 -3.5 ________ = n n = 31.286 Answer:
Fred will weigh under 300 pounds 32 weeks into his weight loss journey. 406-357= 49 Although Fred will be unable to withdraw his money,
he is curious about the value he will have at certain times. a) How much money will have accumulated in Fred's
bank account at the end of his weight loss goal?
a = 100(1.08) 12 12 a 12 100(2.52) = a 12 = 251.82 Answer:
Fred will have accumulated $251.82
in his bank account. To reward himself for losing weight, Fred plans on spending $2000 of the money he will save on a new wardrobe. When will he have saved atleast $2000? 2000 = 100(1.08) n 20 = 1.08 n ln 20 = n ln 1.08 ln 20 ln 1.08 = n _______ n = 38.9 Answer:
Fred will have atleast $2000 dollars in his
bank account 39 weeks after his deposit. Thanks to sequences and series, Fred was able to lose
weight and accumulate money.Take another look at the
previous Fred, and now see the new one. I knew I was beautiful, just deep down inside. Common Ratio: 1.08