## anonymous one year ago Identify the sequence graphed below and the average rate of change from n = 1 to n = 3. coordinate plane showing the point 1, 8, point 2, 4, point 4, 1, and point 5, .5

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1. anonymous

2. anonymous

$a_1=8=2^3$ $a_2=4=2^2$ $a_4=1=2^0$ $a_5=0.5=2^{-1}$ this one's not in there but you should see the pattern well enough to write the sequence $a_3=2=2^1$

3. anonymous

@peachpi those look like none of my question choices. im so confued

4. anonymous

the pattern between points is multiplying by ½, so that's the common ratio, r. The sequence is geometric. The formula for a geometric sequence is $a_n=a_1 r^{n-1}$

5. anonymous

r is ½. a_1 is the first term of the sequence

6. anonymous

Identify the sequence graphed below and the average rate of change from n = 1 to n = 3. coordinate plane showing the point 1, 8, point 2, 4, point 4, 1, and point 5, .5 A) an = 8(one half)n − 1; average rate of change is −3 B) an = 10(one half)n − 1; average rate of change is 3 C)an = 8(one half)n − 1; average rate of change is 3 D) an = 10(one half)n − 1; average rate of change is −3 Those are my answer choices @peachpi

7. anonymous

ok. use the formula I just put up to get a formula for a_n

8. anonymous

|dw:1435250004835:dw|

9. anonymous

okay then then what

10. anonymous

@peachpi what would the correct answer be

11. Michele_Laino

your terms represent a geometric sequence, whose first term is 8 and the constant is 1/2. Now the general term of a geometric sequence is given by the subsequent formula: $\Large {a_n} = {a_1}{q^{n - 1}}$ please substitute q=1/2 and a_1=8, what do you get?

12. anonymous

4?

13. Michele_Laino

hint: $\Large {a_n} = {a_1}{q^{n - 1}} = 8 \times {\left( {\frac{1}{2}} \right)^{n - 1}}$ am I right?

14. anonymous

yes

15. Michele_Laino

16. anonymous

A) an = 8(one half)n − 1; average rate of change is −3 B) an = 10(one half)n − 1; average rate of change is 3 C)an = 8(one half)n − 1; average rate of change is 3 D) an = 10(one half)n − 1; average rate of change is −3 out of these which woud it be?

17. Michele_Laino

for example if we set n=2, we get: $\Large {a_2} = 8 \times {\left( {\frac{1}{2}} \right)^{2 - 1}} = 8 \times \frac{1}{2} = 4$ similarly for other terms

18. Michele_Laino

if we set n=3, we get: $\Large {a_3} = 8 \times {\left( {\frac{1}{2}} \right)^{3 - 1}} = 8 \times \frac{1}{{{2^2}}} = 8 \times \frac{1}{4} = 2$

19. anonymous

still confused for what the avg. rate of change would be

20. Michele_Laino

now the requested change rate, can be this:

21. anonymous

- 3 or 3??

22. Michele_Laino

$\large r = \frac{{{a_1} + {a_2} + {a_3} + {a_4}}}{4} = \frac{{8 + 4 + 2 + 0.5}}{4} = ...$

23. anonymous

3.625

24. Michele_Laino

that's right!

25. anonymous

so the correct answer is C?

26. Michele_Laino

yes I think so!