A recursive rule for an arithmetic sequence is a1 = -4; an = an - 1 + 11

Mathematics

1 answer:

STALIN [3.7K]2 years ago

7 0

Step-by-step explanation:

a1 is already defined : a1 = -4

since an = an-1 + 11, we know d (the constant being added from term to term) is 11.

d = 11

the basic iterative rule is also already defined :

an = an-1 + 11

but we can always also express this in terms of a1 :

an = a1 + 11×(n-1)

therefore,

a10 = -4 + 11×9 = -4 + 99 = 95

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2 years ago

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Usimov [2.4K]

Answer:

Part a. t = 7.29 years.

Part b. t = 27.73 years.

Part c. p = $3894.00

Step-by-step explanation:

The formula for continuous compounding is: A = p*e^(rt); where A is the amount after compounding, p is the principle, e is the mathematical constant (2.718281), r is the rate of interest, and t is the time in years.

Part a. It is given that p = $2000, r = 2.5%, and A = $2400. In this part, t is unknown. Therefore: 2400 = 2000*e^(2.5t). This implies 1.2 = e^(0.025t). Taking natural logarithm on both sides yields ln(1.2) = ln(e^(0.025t)). A logarithmic property is that the power of the logarithmic expression can be shifted on the left side of the whole expression, thus multiplying it with the expression. Therefore, ln(1.2) = 0.025t*ln(e). Since ln(e) = 1, and making t the subject gives t = ln(1.2)/0.025. This means that t = 7.29 years (rounded to the nearest 2 decimal places)!!!

Part b. It is given that p = $2000, r = 2.5%, and A = $4000. In this part, t is unknown. Therefore: 4000 = 2000*e^(2.5t). This implies 2 = e^(0.025t). Taking natural logarithm on both sides yields ln(2) = ln(e^(0.025t)). A logarithmic property is that the power of the logarithmic expression can be shifted on the left side of the whole expression, thus multiplying it with the expression. Therefore, ln(2) = 0.025t*ln(e). Since ln(e) = 1, and making t the subject gives t = ln(2)/0.025. This means that t = 27.73 years (rounded to the nearest 2 decimal places)!!!

Part c. It is given that A = $5000, r = 2.5%, and t = 10 years. In this part, p is unknown. Therefore 5000 = p*e^(0.025*10). This implies 5000 = p*e^(0.25). Making p the subject gives p = 5000/e^0.25. This means that p = $3894.00(rounded to the nearest 2 decimal places)!!!

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3 years ago

I need help on this also could I get an explanation on how you solved it? Please don't take my points ill get u banned. :P

kenny6666 [7]

Answer:

1/2

Step-by-step explanation:

4 is the total right and 5/7 make it half so it will be 1/2. hope this helps!

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2 years ago

Read 2 more answers

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