## anonymous 5 years ago Write the nth term of the arithmetic sequence as a function of n. a[1]=8, a[k+1]=a[k]+7

1. anonymous

The formula for the nth term of an arithmetic sequence is a[n] = a[1]+(n-1)d. You know that d= a[k+1]-a[k] = 7, and a[1]=8, so the nth term is a[n] = 8 + 7(n-1)

2. anonymous

ok so I was close but the problem is that none of the answers I can choose from match with that...let me show you my choices...

3. anonymous

a. a[n]=15+7n b. a[n]=1+7n c. a[n]=8+7n d. a[n]=1+7(n-1) e. a[n]= -1+8n

4. anonymous

If you expand the solution i sent, you'll find a[n] = 8 +7n - 7 = 1 + 7n...answer b.

5. anonymous

oh oh ok sorry about that after I posted it I figured that out thank you and I am your fan now:)

6. anonymous

No worries.

7. anonymous

do you understand how to use the sigma notation?

8. anonymous

Yes.

9. anonymous

Use sigma notation to write the sum. (1/3.2)+(1/4.3)+...+(1/7.6)

10. anonymous

a. $\sum_{n=1}^{5}$ (1/(n+1)(n+2))

11. anonymous

It will be sum from n=3 to 7 of (10/11n-1).

12. anonymous

b. $\sum_{n=1}^{5}(1/(n(n+1)))$

13. anonymous

ok thank you!

14. anonymous

Do you need an explanation?

15. anonymous

Yes that would be helpful... I mean I kinda get it but it wouldn't hurt anything

16. anonymous

The denominator is in the form of some number n + (n-1)/10 (e.g. 3.2 = 3 + (3-1)/10). You then just take the reciprocal of n+(n-1)/10 and use sigma notation for n = 3 to 7.

17. anonymous

I just cleaned up the fraction before using sigma.

18. anonymous

oh ok makes it sound alot easier thanks!

19. anonymous

$\sum_{n=3}^{7}1/[n+(n-1)/10]$

20. anonymous

Find the sum of the infinite series. $\sum_{i=1}^{\infty}4(-1/4)^i$ a.undefined b.-4/3 c.4 d.8/5 e.-4/5

21. anonymous

I'm pretty sure the answer's -4/5, but I want to check something.

22. anonymous

okay...

23. anonymous

Yes...I don't know what level of maths you're doing, but first you need to ensure that the series is convergent. Since it's absolutely convergent, it will be convergent. It also means you can split the sum up into the positive and negative components and use the formula for the limiting value in a geometric series to determine each of the sums. You then end up with -4/5. Do you know how to do this?