1. ## Advanced functions question help

I need help with these advanced functions problems

State the Common Ratio of the following Geometric sequence
3/4 , 3/10 , 3/25 , 6/125

2. In the Arithmetic Sequence below, X = ___
100 , ___ , _X_ , 64

3. For the Geometric Sequence below, X = ___
_X_ , 48 , ___ , ___ , 6

4. Given the sequence 15 , 9 , 3 , -3 ... t 20 = ___

5. Given the sequence 27/8 , 9/4 , 3/2 , 1 ... t 14 = ___ (write as a fraction)

6. State the next 3 terms and state the pattern in WORDS:
a) 4, 9, 15, 22, ....
b) 1, -3, 9, -27, ....

7. Write the first five terms of the sequence defined by the recursive formula:

t1 = 2 , tn = 1 / tn-1

8. For the geometric series 6 + 3 + 3/2 + 3/4 + .... find: (leave you answer as a fraction in lowest terms)
a) the tenth term
b) the sum of the first ten terms

9. In a geometric sequence t5 = 48 and t8 = 384. Find tn.

10. Evaluate: 20 + 14 + 8 + ..... + (-70)

11. In an arithmetic series t1 = 6 and S9 = 108. Find the common difference and sum of the first 20 terms.

12. In an arithmetic series, S11 = 297 and S24 =1428, find tn.

13. A doctor prescribes 200 mg of medication on the first day of treatment. The dosage is halved each day for one week. To the nearest milligram what is the total amount of medication taken by the patient after 1 week?

2. Originally Posted by temour123
I need help with this advanced functions problem

The first term in a sequence of number is t1 = 5. The terms that follow are defined by the formula: tn - tn-1 = 2n +3. Determine the value of t50.
Hi temour123,

I'm having a little difficulty deciphering your notation. Is this what you have?

$t_1=5$ (First Term)

$t_n-t_{n-1}=2n+3$ (Common Difference)

If the 1st term is 5, then the 2nd term will be $2(2)+3=7$, etc. So, the common difference (d) is 2.

Use this formula to calculate the nth term (50th) term:

$t_n=t_1+(n-1)d$

$t_{50}=5+(50-1)2$

3. Hello,
Originally Posted by masters
Hi temour123,

I'm having a little difficulty deciphering your notation. Is this what you have?

$t_1=5$ (First Term)

$t_n-t_{n-1}=2n+3$ (Common Difference)

If the 1st term is 5, then the 2nd term will be $2(2)+3=7$, etc. So, the common difference (d) is 2.

Use this formula to calculate the nth term (50th) term:

$t_n=t_1+(n-1)d$

$t_{50}=5+(50-1)2$
No !

$t_2-t_1=2(2)+3=7 \Rightarrow t_2=5+7=12$

This is not a simple arithmetic progression !

You can see that $t_n-t_1=t_n-t_{n-1}+t_{n-1}-t_{n-2}+t_{n-2}-\dots+t_2-t_1=\sum_{k=2}^{n} [t_k-t_{k-1}]=\sum_{k=2}^n [2k+3]$

$t_n-t_1=2 \sum_{k=2}^n k+3 \sum_{k=2}^n 1=2 \left(\sum_{k=1}^n k-1\right)+3 (n-1)=2 \left(\frac{n(n+1)}{2}-1\right)+3(n-1)$

$t_n-5=2 \left(\frac{n^2+n-2}{2}\right)+3n-3$

Thus $t_n=n^2+n-2+3n-3+5=n^2+4n=n(n+4)$

then just let n=50

5. Originally Posted by temour123
1. Halley's comet appears in the sky approximately once every 77 years. If the comet was seen in by Astronomer Edmund Halley in 1531. How many times has the comet been spotted since?
What is the number of years between 2009 and 1531? (Hint: Subtract.)

How many periods of 77 fit within this period? (Hint: Divide, and ignore the remainder.)

Originally Posted by temour123
2. The disappearance of dinosaurs occurred about 65 million years ago. Scientists have found that mass extinction's occur roughly every 26 million years apart. If this theory is correct, estimate when the next mass extinction should occur.
What is 65 - 26? What do you get if you subtract 26 from that result?

Originally Posted by temour123
3. Canada's population 32.8 million and is growing by approximately 1% per year. Predict the population of Canada in 10 years.
If you are familiar with the compounded-growth formula, A = P(1 + r/n)^(nt), use that, with P = 32.8, r = 0.01, n = 1, and t = 10. Otherwise, find one percent of 32.8, and add this to 32.8. Then find one percent of that, and add it to your previous total. Keep going until you've done ten years' worth.

Originally Posted by temour123
4. Ice Dreams finds its profit from the sale of ice cream increases by $30 per week during the 9 weeks of student summer holidays. Find the profit for the summer season if the profit for the first week of the summer is$100.
If the first week was $100 and the next week was$30 more, then what what the second week?

If the next week was $30 more, then what was the third week? Keep going, until you have the values for each of the nine weeks. Then add the nine values to get the total for the summer. Originally Posted by temour123 5. During the two months of the summer holiday, you find a summer job that pays$160 per week with a $10 a week raise. How much money will be made by the end of the summer? This one work very much like exercise (4) above. Originally Posted by temour123 6. Your grandmother offers you$1 on the first day of March break and offers to double it each day of the break to help her with chores in her house. If you were to help her for 7 days over the break, how much money would you get at the end of day 7?
This one works similarly to exercises (4) and (5), except that you're multiplying each time, instead of adding.

6. Thread closed as a result of many rules being broken.