SOLUTION: What is the smallest 4-digit number in the following sequence? 5, 14, 29, 50, 77, …

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Question 1137872: What is the smallest 4-digit number in the following sequence?
5, 14, 29, 50, 77, …

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
What is the smallest 4-digit number in the following sequence?
5, 14, 29, 50, 77, …
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%5Bn%5D=3n%5E2%2B2


We set that greater than or equal to 1000


3n%5E2%2B2%3E=1000

3n%5E2%3E=998

Divide thru by 3

n%5E2%3E=%22332.6666666...%22

n+%3E=+%2218.23915203...%22

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

So we substitute n=19 in the general term

a%5B19%5D=3%2A19%5E2%2B2=1085


Edwin