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A sequence is formed by adding $2$ to the triple of the previous term. If the first term is $1$, how many multiples of $6$ less than $10{,}000$ would be terms of the sequence?

 Dec 19, 2020
 #1
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A sequence is formed by adding 2 to the triple of the previous term. If the first term is 1 , how many multiples of 6 less than 10000  would be terms of the sequence?

 

Do you undestand the question?

 

First term = 1

2nd term  =1 x 3 + 2 = 5

3rd term  =5 x 3 + 2 = 17

4th term   =17 x 3 + 2 = 53

5th term =53 x 3 + 2 = 161

6th term=161 x 3 + 2 = 485

7th term=485 x 3 + 2 = 1457

8th term=1457 x 3 + 2 =4373

9th term=4373 x 3 + 2 =Goes over 10,000

 

Of the 8 terms, how many of them are multiple of 6? Or are divisible by 6? Use your calculator and find out!.

 Dec 19, 2020
 #2
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Any number divisible by 6 is also divisible by 3.

 

If you add 2 to any multiple of 3 the result is not divisible by 3.

 

Hence none of the numbers in the sequence are divisible by 6.

 Dec 19, 2020

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