Math Help - Series and Sequences

1. Series and Sequences

Need some help with these plz x/

1) The 10th term of an arithmetic sequence is 30 and the sum of the first six terms is 3. Calculate the first three terms of the sequence.

2) The expressions $m^2 - 4$ and $m + 2$ are the first two terms in a geometric seqeunce

2.1 Show that the third term is $\frac{m+2}{m-2}$
2.2 Calculate the value of $m$ of the sequnce is [math \frac{1}{2} [/tex]
2.3 Write down the numeric values of the 1st three terms of the seqeunce

Thanks alot

2. Originally Posted by NeF
Need some help with these plz x/

1) The 10th term of an arithmetic sequence is 30 and the sum of the first six terms is 3. Calculate the first three terms of the sequence.
The sequence shall be,
$a,a+k,a+2k,....$
Then, the 10th term is,
$a+9k=30$
The sum of the first 6 is,
$a+(a+k)+....+(a+5k)=6a+15k=3$
Thus,
$a+9k=30$
$6a+15k=3$
Solve these equation and you will get the values.

3. Originally Posted by NeF
2) The expressions $m^2 - 4$ and $m + 2$ are the first two terms in a geometric seqeunce

2.1 Show that the third term is $\frac{m+2}{m-2}$
The constant ratio is,
$\frac{m+2}{m^2-4}=\frac{m+2}{(m+2)(m-2)}=\frac{1}{m-2}$
Thus, the third term is the second term multiplied by the constant ratio, thus,
$\frac{1}{m-2}(m+2)=\frac{m+2}{m-2}$