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anonymous
 one year ago
Find an equation for the nth term of the arithmetic sequence.
a19 = 58, a21 = 164
anonymous
 one year ago
Find an equation for the nth term of the arithmetic sequence. a19 = 58, a21 = 164

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Nnesha
 one year ago
Best ResponseYou've already chosen the best response.2hey:=) we need common difference and first term to write an equation arithmetic equation \[\huge\rm a_n = a_1 + (n1)d\] where a_1 = first term d=common difference n= term that we have to find

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.2given 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

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.2your turn:=) write an equation when n =21 just like i did for n=19 :=)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0lets see, 164 = a1 (21  1)d ?

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.2perfect! \[\huge\rm 164 = a_1 +(\color{Red}{211})d\] solve parentheses \[\large\rm 164 = a_1 +(\color{Red}{20})d\] this is our 2nd equation first one is \[\huge\rm 58 = a_1 +(\color{Red}{191})d\] \[\large\rm 58 = a_1 +(\color{Red}{18})d\]

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.2\[\large\rm 58 = a_1 + \color{Red}{18} d\]\[\large\rm 164 = a_1 + \color{Red}{20} d\] we will use elimination method to solve this equation :=) so subtract equation one from equation 2 dw:1444396691116:dw

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.2for 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

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.2hmm how did you get 2 d ?

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.2remember we multiplied 2nd equation by negative so it's dw:1444396988124:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oops, i thought it was 18 okay so, 12d = 106 ?

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.2hmm right but keep it in fraction dw:1444397180870:dw 53/6 now substitute this into the equation for d to find first term

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.2\[\huge\rm a_n=a_1 +(n1)d\] find first term substitute 53/6 for d

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0a_n = a_1 + (n  1)53/6 ... im kinda lost

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.2well n= number of term that we have to find so to find first term substitute n for 1

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0a_1 = a_1+ ( n  1) 53/6

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.2\[\large\rm 58 = a_1 + \color{Red}{18} d\]\[\large\rm 164 = a_1 + \color{Red}{20} d\] we can use one of these equation to find a_1 not original equation

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Mathway.com is like a caculetor but is a web

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.2lets use first one \[\rm a_1 +18d =58\] substitute d for 53/6 to find a_1

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.2i'm pretty sure i'm doing something wron ugh sorry let me see

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i see, a_1 + 18(53/6) = 58 would a_1 be 159 ..?

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.2dw:1444397762260:dw you were right it's 18

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.2i'm sorry. it was a_1 + (18 1)d = a_1 + `18d`

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.2now \[\rm a_1 +18(53) = 58\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay sooo, a_1 + 18(53) = 58 a_1 + 954 =  58

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.2looks good solve for a_1

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0soooo then would it be.. a_n = 896 53 (n1) ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0woohooo! thank you so much!

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.2np :=) btw you can distribute (n1 ) by 53

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.2\[\rm a_n = 896 53n+53\] combine like terms
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