Question 1137872
What is the smallest 4-digit number in the following sequence?
5, 14, 29, 50, 77, …
<pre>
They're all 2 more than a multiple of 3, so we subtract 2 from each

3, 12, 27, 48, 75

Divide each by 3

1, 4, 9, 16, 25

That's the perfect squares, so the sequence 5, 14, 29, 50, 77, …

has general term


{{{a[n]=3n^2+2}}}


We set that greater than or equal to 1000


{{{3n^2+2>=1000}}}

{{{3n^2>=998}}}

Divide thru by 3

{{{n^2>="332.6666666..."}}}

{{{n >= "18.23915203..."}}}

So 19 is the smallest integer for which the
sequence has 4 digits.

So we substitute n=19 in the general term

{{{a[19]=3*19^2+2=1085}}}


Edwin</pre>