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anonymous

  • one year ago

Find an equation for the nth term of the arithmetic sequence. a19 = -58, a21 = -164

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  1. anonymous
    • one year ago
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    @Nnesha

  2. Nnesha
    • one year ago
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    hey:=) we need common difference and first term to write an equation arithmetic equation \[\huge\rm a_n = a_1 + (n-1)d\] where a_1 = first term d=common difference n= term that we have to find

  3. Nnesha
    • one year ago
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    given terms are a_{19}= -58 a_{21} = -164 plug this into the equation \[\large\rm a_\color{ReD}{{19}}=a_1 +(\color{ReD}{19}-1)d\] 19th term so we substitute n for 19 and a_{19} equal to -58 we can replace a_{19} with -58 \[\large\rm -58=a_1 +(\color{ReD}{19}-1)d\] same for a_{21} write an equation when n =21

  4. Nnesha
    • one year ago
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    your turn:=) write an equation when n =21 just like i did for n=19 :=)

  5. Nnesha
    • one year ago
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    make sense ??

  6. anonymous
    • one year ago
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    lets see, -164 = a1 (21 - 1)d ?

  7. Nnesha
    • one year ago
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    perfect! \[\huge\rm -164 = a_1 +(\color{Red}{21-1})d\] solve parentheses \[\large\rm -164 = a_1 +(\color{Red}{20})d\] this is our 2nd equation first one is \[\huge\rm -58 = a_1 +(\color{Red}{19-1})d\] \[\large\rm -58 = a_1 +(\color{Red}{18})d\]

  8. Nnesha
    • one year ago
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    \[\large\rm -58 = a_1 + \color{Red}{18} d\]\[\large\rm -164 = a_1 + \color{Red}{20} d\] we will use elimination method to solve this equation :=) so subtract equation one from equation 2 |dw:1444396691116:dw|

  9. Nnesha
    • one year ago
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    for elimination method we should change the sign of one of the equation in other words multiply by negative one now we have a_1 - a_1 we can cancel it out |dw:1444396859763:dw| now combine other terms

  10. anonymous
    • one year ago
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    2d = -222 ?

  11. Nnesha
    • one year ago
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    hmm how did you get 2 d ?

  12. Nnesha
    • one year ago
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    remember we multiplied 2nd equation by negative so it's |dw:1444396988124:dw|

  13. anonymous
    • one year ago
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    oops, i thought it was 18 okay so, 12d = -106 ?

  14. Nnesha
    • one year ago
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    right now solve for d

  15. anonymous
    • one year ago
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    -8.833

  16. Nnesha
    • one year ago
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    hmm right but keep it in fraction |dw:1444397180870:dw| -53/6 now substitute this into the equation for d to find first term

  17. Nnesha
    • one year ago
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    \[\huge\rm a_n=a_1 +(n-1)d\] find first term substitute -53/6 for d

  18. anonymous
    • one year ago
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    a_n = a_1 + (n - 1)-53/6 ... im kinda lost

  19. Nnesha
    • one year ago
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    hmm why ?

  20. Nnesha
    • one year ago
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    well n= number of term that we have to find so to find first term substitute n for 1

  21. anonymous
    • one year ago
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    a_1 = a_1+ ( n - 1) -53/6

  22. Nnesha
    • one year ago
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    i seeeee

  23. Nnesha
    • one year ago
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    \[\large\rm -58 = a_1 + \color{Red}{18} d\]\[\large\rm -164 = a_1 + \color{Red}{20} d\] we can use one of these equation to find a_1 not original equation

  24. anonymous
    • one year ago
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    Mathway.com is like a caculetor but is a web

  25. Nnesha
    • one year ago
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    lets use first one \[\rm a_1 +18d =-58\] substitute d for -53/6 to find a_1

  26. Nnesha
    • one year ago
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    i'm pretty sure i'm doing something wron ugh sorry let me see

  27. anonymous
    • one year ago
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    i see, a_1 + 18(-53/6) = -58 would a_1 be -159 ..?

  28. Nnesha
    • one year ago
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    |dw:1444397762260:dw| you were right it's 18

  29. anonymous
    • one year ago
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    ooooooooooooh lol!

  30. Nnesha
    • one year ago
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    i'm sorry. it was a_1 + (18 -1)d = a_1 + `18d`

  31. Nnesha
    • one year ago
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    now \[\rm a_1 +18(-53) = -58\]

  32. anonymous
    • one year ago
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    okay sooo, a_1 + 18(-53) = -58 a_1 + -954 = - 58

  33. anonymous
    • one year ago
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    a_1 = 896

  34. Nnesha
    • one year ago
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    looks good solve for a_1

  35. anonymous
    • one year ago
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    soooo then would it be.. a_n = 896 -53 (n-1) ?

  36. Nnesha
    • one year ago
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    right :=)

  37. anonymous
    • one year ago
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    woohooo! thank you so much!

  38. Nnesha
    • one year ago
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    np :=) btw you can distribute (n-1 ) by -53

  39. Nnesha
    • one year ago
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    \[\rm a_n = 896 -53n+53\] combine like terms

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