Question 628105: Given the sequence 3,7,13,21,31,...,183,k,241,... find k
a.201
b.203
c.207
d.211
e.223
Answer by fcabanski(1391)   (Show Source):
You can put this solution on YOUR website! When faced with a long sequence, find the pattern by looking at the first few terms. It's clear the difference between each term is 4,6,8,10... moving up consecutive even numbers. The difference between 183 and k must be one even number before the difference between 241 and k.
Because this is multiple choice there's no need to count or figure out where 183,k, and 241 are in the sequence. Check each choice.
201: 201-183 = 18. The difference between k=201 and the next term has to be 20 to continue the sequence. But 241-201 = 30. It doesn't work.
Check each one the same way. Only 211 works. 211-183=28 and 241-211 = 30, which is consistent with the sequence.
Hope the solution helped. Sometimes you need more than a solution. Contact fcabanski@hotmail.com for online, private tutoring, or personalized problem solving (quick for groups of problems.)
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