Question: Advanced Functions Math questions View Single Post
 Unknown008 Posts: 8,147, Reputation: 3745 Uber Member #4 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 are, 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.