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yummydum

Using sigma notation, describe the total length of 7 pictures hung side-by-side. Then find the total length the pictures occupy along the wall if the first picture has a length of 10 inches and the length of each successive picture is 4 inches longer than the previous one.

  • one year ago
  • one year ago

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  1. yummydum
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    @hartnn

    • one year ago
  2. hartnn
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    let l1 to l7 be length of pics. from n=1 to 7, l_n and sum notation : \(\sum \limits_{n=1}^7l_n\) is your 1st part.

    • one year ago
  3. ParthKohli
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    Hint: for the first part, denote the length of the seven pictures by a sequence \(a_1, a_2 \cdots a_7\)

    • one year ago
  4. hartnn
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    l1 =10 and common difference d =4

    • one year ago
  5. yummydum
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    rightI got that but for the equation..?

    • one year ago
  6. hartnn
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    you need to find n'th tern l_n with l_1 =10 , d = 4 \(l_n = l_1+(n-1)d\)

    • one year ago
  7. yummydum
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    10, 14, 18,..\[a_n=(10)-(n-1)(4)\]\[a_n=10-4n+4\]\[a_n=14-4n\]\[\sum_{n=1}^{7}~14n-4\]yes?

    • one year ago
  8. hartnn
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    middle sign is + ln = 6+4n

    • one year ago
  9. yummydum
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    oh ...i knew that..

    • one year ago
  10. hartnn
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    now can you solve the summation ?

    • one year ago
  11. hartnn
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    \(\sum 6+4\sum n\)

    • one year ago
  12. ParthKohli
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    The worst pain, after the famines and diseases, is typing on an iPad. :-(

    • one year ago
  13. hartnn
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    know whats \(\sum n=..?\)

    • one year ago
  14. yummydum
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    wow it wrote that weird.. \[\large\sum_{n=1}^{7} ~6+4n~~ \implies~~154\]

    • one year ago
  15. ParthKohli
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    I don't know, just pointing out that a common mistake students sometimes make is that they do \(\sum 6 = 6\) when it's not.

    • one year ago
  16. hartnn
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    i also get 154

    • one year ago
  17. ParthKohli
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    You didn't make that mistake though, nice :-)

    • one year ago
  18. yummydum
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    err..what? i did \([6+(4\times1)]+[6+(4\times2)]+[6+(4\times3)]+\)\([6+(4\times4)]+[6+(4\times5)]+[6+(4\times6)]+[6+(4\times7)]\)

    • one year ago
  19. ParthKohli
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    You are right.

    • one year ago
  20. yummydum
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    10+14+18+22+26+30+34=154.....yup :)

    • one year ago
  21. ParthKohli
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    I never said you were wrong lol, just pointing out a common mistake.

    • one year ago
  22. ParthKohli
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    Good stuff :-)

    • one year ago
  23. yummydum
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    lol, thanks guys!

    • one year ago
  24. yummydum
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    whats 8(n+3)??

    • one year ago
  25. yummydum
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    10+14+18+22+26+30+34=154 ....is that not right?

    • one year ago
  26. yummydum
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    o.O

    • one year ago
  27. yummydum
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    lol no probs

    • one year ago
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