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2 years ago

Given a geometric sequence with a1 = 3 and r = 0.5, write the first three terms of the sequence

1 answer:

8 0

In a geometric sequence, the numbers are found by multiplying each number by a fixed amount called a common ratio(r).

a1....this is ur first number....so since a1 = 3, ur first number is 3...and to find ur next numbers, multiply each number by r, the common ratio (which equals 0.5)

first number = 3.......3 x 0.5 = 1.5
second number = 1.5......1.5 x 0.5 = 0.75
third number = 0.75

si the first 3 terms are : 3, 1.5, 0.75

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3 years ago

Consider a home mortgage of $225,000 at a fixed APR of 4.5 % for 30 years. a. Calculate the monthly payment. b. Determine the

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The formula for the monthly payment.....

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Here annual interest rate is given as 4.5%

So, the monthly interest rate $=\frac{4.5\%}{12}= 0.375\% = 0.00375$

Total number of months $= (30*12)months=360 months$

Also given that, the principal amount is $225000

a. So, the monthly payment will be.....

$M= \frac{P(1+r)^nr}{[(1+r)^n] -1}\\ \\ M= \frac{225000(1+0.00375)^3^6^0*0.00375}{(1+0.00375)^3^6^0 -1}\\ \\ M= \frac{225000(1.00375)^3^6^0*0.00375}{(1.00375)^3^6^0 -1} \\ \\ M \approx 1140$

Thus, the monthly payment will be approximately $1140

b. The total amount paid over the term of the loan will be: $\$ 1140*360 months = \$ 410400$

c. As the principal amount was $225000 , so the amount of interest $= (\$ 410400- \$ 225000)= \$ 185400$

So, the percentage of amount that is paid toward the principal $=\frac{225000}{410400}*100\% =54.82\%$

and the percentage of amount that is paid toward the interest $=\frac{185400}{410400}*100\%=45.18\%$

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