anonymous
  • anonymous
Write the nth term of the arithmetic sequence as a function of n. a[1]=8, a[k+1]=a[k]+7
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • 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)
anonymous
  • 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...
anonymous
  • 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

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anonymous
  • anonymous
If you expand the solution i sent, you'll find a[n] = 8 +7n - 7 = 1 + 7n...answer b.
anonymous
  • anonymous
oh oh ok sorry about that after I posted it I figured that out thank you and I am your fan now:)
anonymous
  • anonymous
No worries.
anonymous
  • anonymous
do you understand how to use the sigma notation?
anonymous
  • anonymous
Yes.
anonymous
  • anonymous
Use sigma notation to write the sum. (1/3.2)+(1/4.3)+...+(1/7.6)
anonymous
  • anonymous
a. \[\sum_{n=1}^{5}\] (1/(n+1)(n+2))
anonymous
  • anonymous
It will be sum from n=3 to 7 of (10/11n-1).
anonymous
  • anonymous
b. \[\sum_{n=1}^{5}(1/(n(n+1)))\]
anonymous
  • anonymous
ok thank you!
anonymous
  • anonymous
Do you need an explanation?
anonymous
  • anonymous
Yes that would be helpful... I mean I kinda get it but it wouldn't hurt anything
anonymous
  • 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.
anonymous
  • anonymous
I just cleaned up the fraction before using sigma.
anonymous
  • anonymous
oh ok makes it sound alot easier thanks!
anonymous
  • anonymous
\[\sum_{n=3}^{7}1/[n+(n-1)/10]\]
anonymous
  • 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
anonymous
  • anonymous
I'm pretty sure the answer's -4/5, but I want to check something.
anonymous
  • anonymous
okay...
anonymous
  • 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?

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