Can someone please put me on the right track to solving these problems? If you can provide an example for at least one of each, I would greatly appreciate it. Thanks so much. Please see attachment. ,:( :confused:

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- Jan 23rd 2007, 05:44 AMfw_mathisArithmetic sequence, geometric sequence, & geometric series
Can someone please put me on the right track to solving these problems? If you can provide an example for at least one of each, I would greatly appreciate it. Thanks so much. Please see attachment. ,:( :confused:

- Jan 23rd 2007, 08:20 AMCaptainBlackQuote:

Question 1:

Use the arithmetic sequence of numbers 2, 4, 6, 8, 10… to find the following:

What is d, the difference between any 2 terms?

the differences can be written:

(4-2)=2, (6-4)=2, (8-6)=2, (10-8)=2.

Quote:

Question 2:

Using the formula for the*n*th term of an arithmetic sequence, what is 101st term?

Therefore the 101-st tem is 1x101=202.

Quote:

Using the formula for the sum of an arithmetic sequence, what is the sum of the first 20 terms?

S(n)=(1/2)n(2a+(n-1)d)

here first term a=2, common difference d=2 and n=20, so:

S(20)=(1/2)x20x(4+19x2)=420

RonL - Jan 23rd 2007, 08:47 AMSoroban
Hello, fw_mathis!

Are you**really**having trouble with these problems?

Do you know what "difference between any two terms" means?

. . And you're expected know the necessary formulas.

So where__exactly__is your difficulty?

Quote:

Using the arithmetic sequence of numbers: $\displaystyle 2,\,4,\,6,\,8,\,10,\,\hdots$ to find the following:

What is $\displaystyle d$, the difference between any two__consecutive__terms?

The difference between 2 and 4 is . . . um . . . 2 ?

The difference between 4 and 6 is . . . er . . . 2 ?

Quote:

Using the formula for the $\displaystyle n^{th}$ term of an arithmetic sequence, what is the $\displaystyle 101^{st}$ term?

The formula for the $\displaystyle n^{th}$ term is: .$\displaystyle a_n\:=\:a + (n-1)d$

. . where $\displaystyle a$ = first term, $\displaystyle d$ = common difference, $\displaystyle n$ = number of terms.

We have: .$\displaystyle a = 2,\:d = 2,\:n = 101$

Therefore: .$\displaystyle a_{101} \;=\;2 + (101-1)2 \;=\;202$

Quote:

Using the formula for the sum of an arithmetic sequence,

. . what is the sum of the first $\displaystyle 20$ terms?

Formula: .$\displaystyle S_n\;=\;\frac{n}{2}\left[2a + (n-1)d\right] $

We have: .$\displaystyle a = 2,\:d = 2,\;n = 20$

Therefore: .$\displaystyle S_{20} \;=\;\frac{20}{2}\left[2(2) + (20-1)2\right] \;=\;420$

I'll let someone else teach you about Geometric Sequences . . .