My Math Forum Determine the formula for the nth term of the sequence?

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 May 20th, 2010, 11:41 AM #1 Newbie   Joined: May 2010 Posts: 5 Thanks: 0 Determine the formula for the nth term of the sequence? t35 = -53.9 and t53 = -21.5 t35 and t53 (the numbers 35 and 53 are suppose to be small. Please show all steps towards solution thanks!!!
May 20th, 2010, 12:29 PM   #2
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Re: Determine the formula for the nth term of the sequence?

Quote:
 Originally Posted by reddd t35 = -53.9 and t53 = -21.5 t35 and t53 (the numbers 35 and 53 are suppose to be small. Please show all steps towards solution thanks!!!
Hi reddd,

You failed to tell us if it is an "arithmetic" or "geometric" sequence!

$.....t_{35}......t_{53}......t_n$

Assuming it is an arithmetic sequence, we need to find the common difference and the 1st term.

$t_n=t_1+(n-1)d$

$t_{53}=t_{35}+(19-1)d$ There are 19 terms between 35th and 53rd terms inclusive.

$-21.5=-53.9+18d$

$d=1.8$

Now, let's find the 1st term.

$t_n=t_1+(n-1)d$

$t_{35}=t_1+(35-1)1.8$

$-53.9=t_1+61.2$

$t_1=-115.1$

Now, to the equation for the nth term: $t_n=-115.1+(n-1)1.8$

If you want, you can expand the right side so that $t_n=1.8n-116.9$.

May 20th, 2010, 12:45 PM   #3
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Re: Determine the formula for the nth term of the sequence?

Quote:
Originally Posted by masters
Quote:
 Originally Posted by reddd t35 = -53.9 and t53 = -21.5 t35 and t53 (the numbers 35 and 53 are suppose to be small. Please show all steps towards solution thanks!!!
Hi reddd,

You failed to tell us if it is an "arithmetic" or "geometric" sequence!

$.....t_{35}......t_{53}......t_n$

Ah sorry; it's an arithmetic sequence.

 May 20th, 2010, 12:50 PM #4 Global Moderator   Joined: Dec 2006 Posts: 19,066 Thanks: 1621 $\text{For an AP, }t_n\,=\,1.8n\,-\,116.9.$ You can get this by solving the simultaneous equations 35d + a = -53.9, 53d + a = -21.9. By the nth term, does the question mean $t_n$ or $t_{n-1}$?

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# Find an equation for the nth term of the arithmetic sequence. -15, -6, 3, 12, ...

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