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 April 1st, 2012, 09:23 AM #1 Newbie   Joined: Feb 2012 Posts: 10 Thanks: 0 Find the units digit The 20th term of an arithmetic sequence exceeds the 12th term by 64. If the units digit of the 20th term is 5, what is the units digit of the 2012th term?
April 1st, 2012, 05:46 PM   #2
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Re: Find the units digit

Hello, josh2499!

Quote:
 The 20th term of an arithmetic sequence exceeds the 12th term by 64. If the units digit of the 20th term is 5, what is the units digit of the 2012th term?

$\text{The 12th term is: }\:a_{12} \:=\:a_1\,+\,11d$
$\text{The 20th term is: }\:a_{20} \:=\:a_1\,+\,19d$

$\text{We are told: }\: a_{20} \:=\:a_{12}\,+\,64$

[color=beige]. . . . . . . [/color]$a_1\,+\,19d \:=\:a_1\,+\,11d\,+\,64 \;\;\;\Rightarrow\;\;\;8d \:=\:64 \;\;\;\Rightarrow\;\;\;d \:=\:8$

$\text{Then: }\:a_{20} \:=\:a_1\,+\,19(8) \:=\:a_1\,+\,152$

$\text{Since }a_{20}\text{ ends in 5, then }a_1\text{ ends in 3: }\:a_1 \,=\,\_\_3.$

$\text{W\!e have: }\:a_{2012} \:=\:a_1\,+\,2011(8) \:=\:\_\_3\,+\,16,088$

$\text{Therefore, the units digit of }a_{2012}\text{ is 1.}$

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