Advanced Math

**azeee100** · April 8th 2009, 04:56 PM

Need help with these questions for a test review.

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?

**Prove It** · April 8th 2009, 05:31 PM

Originally Posted by azeee100

Need help with these questions for a test review.

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?

These look pretty basic... have you tried any at all?

**Jhevon** · April 8th 2009, 05:32 PM

First see: Arithmetic progression - Wikipedia, the free encyclopedia

and

Geometric progression - Wikipedia, the free encyclopedia

Originally Posted by azeee100

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

t1 = 2 , tn = 1 / tn-1

please use parentheses!

i am sure you meant $t_n = \frac 1{t_{n - 1}}$ . in that case, type: t_n = 1/t_(n - 1) or better yet, use {} brackets. even better, use {} brackets and put LaTeX tags around everything. see the last link in my signature.

anyway, if you're about to do a test, surely you can at least do this type of problem by now.

you want the list $t_1,~t_2,~t_3,~t_4,~t_5$

for $t_2$ , plug in $n = 2$ in the formula for $t_n$ . here you get $t_{\color{red}2} = \frac 1{t_{{\color{red}2} - 1}} = \frac 1{t_1} = \frac 12$

now do the same for the others.

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

see the second link i gave you at the start of this thread. here, your a = 6 and your r = 1/2

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

again, see the second link for the general form. and apply a similar method to the one used here to find $t_n$

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

see the first link i gave you at the beginning of this thread. here $a_1 = 20$ and $d = -6$

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

again, see the first link i gave

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

ditto

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?

note that the dosage follows a geometric sequence, with $a = 200$ and $r = \frac 12$ . you want the sum of the first 7 terms of this sequence

**Prove It** · April 8th 2009, 05:39 PM

Originally Posted by Jhevon

you want the list $t_1,~t_2,~t_3,~t_4,~t_5$

for $t_2$ , plug in $n = 2$ in the formula for $t_n$ . here you get $t_{\color{red}2} = \frac 1{t_{{\color{red}2} - 1}} = \frac 1{t_1} = 1$

now do the same for the others.

Actually it's...

$t_2 = \frac{1}{t_1} = \frac{1}{\color{red}2}$ .

**Jhevon** · April 8th 2009, 05:47 PM

Originally Posted by Prove It

Actually it's...

$t_2 = \frac{1}{t_1} = \frac{1}{\color{red}2}$ .

yes, fixed it

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