Alf needs to borrow $15,000 to pay for his college tuition. He can borrow the money from his parents at a rate of 3.55% interest compounded annually for 4 years, or he can borrow from his
local bank at a rate of 3.50% interest compounded continuously for 4 years
Manipulation of Numerical Data

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Ответ:

pankajyadav7402

09.09.2021

Mathematics

see explanation

Step-by-step explanation:

The explicit formula for a geometric sequence is

$a_{n}$ = a₁ $(r)^{n-1}$

where a₁ is the first term and r the common ratio

Here a₁ = 200 and r = $\frac{a_{2} }{a_{1} }$ = $\frac{100}{200}$ = $\frac{1}{2}$ , then

$a_{n}$ = 200 $(\frac{1}{2}) ^{n-1}$ ← explicit formula

The 15 th term is then

a₁₅ = 200 × $(\frac{1}{2}) ^{14}$

= 200 × $\frac{1}{16384}$

= $\frac{200}{16384}$ ← divide numerator/ denominator by 8

= $\frac{25}{2048}$

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Alf needs to borrow $15,000 to pay for his college tuition. He can borrow the money from his parents at a rate of 3.55% interest compounded annually for 4 years, or he can borrow from his local bank at a rate of 3.50% interest compounded continuously for 4 years Manipulation of Numerical Data