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In a sequence of ten terms, each term (starting with the third term) is equal to the sum of the two previous terms. The seventh term is equal to 6. Find the sum of all ten terms.

 

 

 

Find the sum of the first 25 terms of the sequence   1,2,-3,4,5,-6,7,8,-9

 

The sequence starting 1, 5, 12, 22, 35,  counts the number of points in each diagram. Find the number of points in the tenth diagram.

 


 

 Feb 22, 2020

Best Answer 

 #1
avatar+18910 
+2

Question #1:  This will be a Fibonacci Sequence:  1, 1, 2, 3, 5, 8, 13, 21, 34, ...

To get the 7th term to be 6, multiply each term by 6/13, giving:

     6/13, 6/13, 12/13, 18/13, 30/13, 78/13, 126/13, 204/13  =  480/13

 

Question #2:  1,2,-3, 4,5,-6, 7,8,-9, 10,11-12, ...

Adding each set of 3 numbers give this sum:  0, 3, 6, 9, ...

This becomes an arithmetic sequence; to get the sum of the (original) 24 numbers:

    Sum  =  8(0 + 21)/2  =  84

Then, you must add the 25th number:  84 + 25  =  109

 

Question #3:  The sequence 1, 5, 12, 22, 35, ...  Is the pentagonal numbers.

A formula to find the nth number is:  Pn =  n(3n - 1)/2

So the 10th number is:  10(3·10 - 1)/2  =  145

 Feb 23, 2020
 #1
avatar+18910 
+2
Best Answer

Question #1:  This will be a Fibonacci Sequence:  1, 1, 2, 3, 5, 8, 13, 21, 34, ...

To get the 7th term to be 6, multiply each term by 6/13, giving:

     6/13, 6/13, 12/13, 18/13, 30/13, 78/13, 126/13, 204/13  =  480/13

 

Question #2:  1,2,-3, 4,5,-6, 7,8,-9, 10,11-12, ...

Adding each set of 3 numbers give this sum:  0, 3, 6, 9, ...

This becomes an arithmetic sequence; to get the sum of the (original) 24 numbers:

    Sum  =  8(0 + 21)/2  =  84

Then, you must add the 25th number:  84 + 25  =  109

 

Question #3:  The sequence 1, 5, 12, 22, 35, ...  Is the pentagonal numbers.

A formula to find the nth number is:  Pn =  n(3n - 1)/2

So the 10th number is:  10(3·10 - 1)/2  =  145

geno3141 Feb 23, 2020

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