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In each blank below a single digit is inserted such that the following six three-digit numbers, in this order, form an arithmetic sequence:
\( 1 \,\underline{\hspace{9pt}}\, \,\underline{\hspace{9pt}}\, \;\;,\;\; \,\underline{\hspace{9pt}}\, \,\underline{\hspace{9pt}}\, 9 \;\;,\;\; 2 \,\underline{\hspace{9pt}}\, 2 \;\;,\;\; \,\underline{\hspace{9pt}}\, 6 \,\underline{\hspace{9pt}}\, \;\;,\;\; 2 \,\underline{\hspace{9pt}}\, \,\underline{\hspace{9pt}}\, \;\;,\;\; \,\underline{\hspace{9pt}}\, 3 \,\underline{\hspace{9pt}} \)
What is the value of the next number in the sequence? 

 Jan 14, 2019
 #1
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The last digit of the common difference is 3

A little trial and error produces......

 

232 + 33 =  265

265 + 33 =  298

298 + 33 =  331

 

232 - 33 = 199

199 - 33 =  166

 

So...the next number is

 

331 + 33 =

 

364

 

 

cool cool cool

 Jan 14, 2019
edited by CPhill  Jan 14, 2019

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