Find the next 3 terms in each sequence or series of numbers. 2+9+28+65+......A clear explaination, please

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embizze | High School Teacher | (Level 1) Educator Emeritus

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Find the next three numbers in the series 2+9+28+65+...

Look at the underlying sequence: 2,9,28,65,...

** Reminder: There are an infinite number of sequences that begin with any given finite number of entries, so this is just one possibility**

(1) Perhaps you start with some well-known sequences and see if any might help:

squares: 1,4,9,16,25,36,...
triangular numbers: 1,3,6,10,15,21,...
cubes: 1,8,27,64,...

We see that each entry in the given sequence is one more than a cube, so possible the sequence is:

2,9,28,65,126,217,344,... `a_n=n^3+1`

So the series will be 2+9+28+65+126+217+344+...

 

 

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