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temour123 · Apr 4, 2009, 01:01 PM

I need help on how to do these questions

1. 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?

Curlyben · Apr 4, 2009, 01:14 PM

Thank you for taking the time to copy your homework to AMHD.
Please refer to this announcement: Ask Me Help Desk - Announcements in Forum : Homework Help

temour123 · Apr 4, 2009, 01:22 PM

Lol I didn't ask you to tell me to not copy my homework I asked for the answers and how to do it so if your mot going to do that then leave

Unknown008 · Apr 5, 2009, 07:32 AM

1. The common ratio is obtained by dividing a term by the previous one. As a check, you can divide another further term by its previous term. The ratio should be the same.

2. Use your formula
$T_n = a + (n-1)d$

where n is the term number. By this, find d, the common difference and obtain T3, the third term by the formula.

If you don't know that formula, do (100 - 64)/3 to obtain the amount removed after each term.

3. Use the formula

$T_n = ar^{n-1$

Find r, the common ratio and solve for the first term.

4. First you must identify the type of sequence. Is it arithmetic or geometric?
When you find the answer, just use the formulae I gave you above, depending on the type of sequence it is. (An AP kind of adds or subtracts a fixed number each time, and a GP either multiplies or divides each time by a fixed number).

5. Same thing as in 4.

6. That you'll have to write it in your own words, from your knowledge of sequences.

7. You are given the first term T1, to obtain the next terms, replace n=2 and n=3 in your given equation.

8. You should be able to do (a) now.
For (b) use the formula $S_n=\frac{a(r^n-1)}{r-1}$ if n>1 or $S_n=\frac{a(1-r^n)}{1-r}$ if |n|<1.

9. That should be easy by now. There's only a simultaneous equation tobe solved.

10. Identify the type of sequence, then use your Sum formulae (for an AP, it is $S_n= \frac{n(T_1+T_l)}{2}$ , where l is the last term.

11. & 12. You should be able to do these by now.

13. This too should be easy now.

brig · Dec 26, 2009, 01:45 PM

1. 2/5
2. 100, 91, 82, 73, 64
3. 96,48,24,12,6
4. -99
5. 1024/59049
6. a) 30, 39, 49, 60, 72 (I'm not sure though)
b) I can't get it!
7. I'm not sure about recursive formulas!
8. a) 3/256
b) -3583/512
9. tn = 1.5(2)^(n-1)
10. -400
11. d=1.5, t20 = 34.5
12. Tn = 5n-3

galactus · Dec 26, 2009, 06:56 PM

This was originally posted back in April. I believe it's a moot point.

But, just for kicks. The recursive formula is

$t_{n}=2, \;\ t_{n}=\frac{1}{t_{n-1}}$

Just plug in:

$t_{2}=\frac{1}{t_{1}}=\frac{1}{2}$

$t_{3}=\frac{1}{t_{2}}=\frac{1}{\frac{1}{2}}=2$

$t^{4}=\frac{1}{t^{3}}=\frac{1}{2}$

and so on.

and so on

The recursion is 2,1/2,2,1/2,2,.