Question

HELP PLEASE
WILL REWARD MEDAL

Write the rule for an arithmetic sequence whose tenth term is 75.

Answer 1

The name of the rule for an arithmetic sequence whose tenth term is 75 is the hyperbolic tangent. The hyperbolic tangent is the solution to the nonlinear boundary value problem.

Answer 2

a+9d=75

Answer 3

so would this rule be acceptable: 75=d(n-1)+a1 where a1 = the first term
but my teacher said that was wrong she said "A rule must have only one variable, you left too many unknowns in the equation. "

Answer 4

@gauravkj could you please explain how you got that

Answer 5

to solve an arithmetic progression we need to variables.. so we need two information.. u gave only one informatio. so u can not solve both variables.. may be dats not the complete
question..

Answer 6

it is the complete question and heres what i put down as an answer the first time:
75=d(n-1)+a1 where a1 is the first term and my teacher said: "A rule must have only one variable, you left too many unknowns in the equation." @gauravkj

Answer 7

here n=10
so a+9d=75.. cant be solved further

Answer 8

@Monica75 you seem to know your stuff in math do you think he is correct

Answer 9

Guys, the problem says to write the rule for an arithmetic sequence whose 10th term is 75. It doesn't say to write the rule for "the" arithmetic sequence! You just to devise any arithmetic sequence whose 10th term is 75.

No, the hyperbolic tangent is not the answer to this problem :-)

Answer 10

dats what i said.. u cant have a specific solution.. u can have infinite many solutio.. take a=3 and d=8.. u r done

Answer 11

@whpalmer4 could you explain to me further and how i can answer this question

Answer 12

@gauravkj except you said it couldn't be solved further, and that's not really true.

Example arithmetic sequences where the 10th term is 75:

\[a_1 = 66, d = 1\]\[66,67,68,69,70,71,72,73,74,75\]
\[a_1=57, d =2\]\[57, 59, 61, 63, 65, 67, 69, 71, 73, 75\]

Answer 13

so how would that be written in a "rule" form ?

Answer 14

So, pick a value of \(d\) that you like, plug it into the equation with \(n=10\) and \(a_n=75\) and solve for \(a_1\):

\[d=8\]\[a_n = (n-1)d + a_1\]\[75=(10-1)8+a_1\]\[75=9*8+a_1\]\[a_1=3\]

Answer 15

People are probably tired of hearing me say this, but attention to detail when reading the problem is crucial! The key to success here was the difference between "the" and "an".

Answer 16

Yes ! that is so true

Answer 17

Or could do it by hand. Say I wanted a sequence with a difference of 5. I write down 75, and count backwards by 5 until I have 10 terms written on my paper (in reverse order, of course):

75 70 65 60 55 50 45 40 35 30
30 is a_1 and 5 is d, or
\[a_n = 5(n-1)+30\]

Answer 18

oh okay i get it now Thank you so much for the easy explanation and the further effort to help me out and help me understand it ! greatly appreciated thanks @whpalmer4 !!!