SOLUTION: The population of a village at the end of consecutive decades was 2173, 2281, 2395, 2514. Show that the population was increasing approximately in G.P.

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Question 1203380: The population of a village at the end of consecutive decades was 2173, 2281, 2395, 2514. Show that the population was increasing approximately in G.P.
Found 3 solutions by ikleyn, math_tutor2020, josgarithmetic:
Answer by ikleyn(52781)   (Show Source):
You can put this solution on YOUR website!
.

Take the ratios of consecutive terms and compare these ratios each to other.

It is what you can easily make WITHOUT ANY HELP FROM OUTSIDE (I hope),
if you know the definition of a G.P.

This problem is not for thinking - - - it is for DOING.

On geometric progressions, see introductory lessons
    - Geometric progressions
    - The proofs of the formulas for geometric progressions
    - Problems on geometric progressions
    - Word problems on geometric progressions
in this site.

Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!

To determine if we have a geometric sequence, we divide each term over its previous term.
The goal is to see if we get the same ratio each time.

r = term2/term1 = 2281/2173 = 1.049701
r = term3/term2 = 2395/2281 = 1.049978
r = term4/term3 = 2514/2395 = 1.049687

We get slightly different r values each time.
The 1.049 portion matches up, but the other decimal digits do not.

So the sequence {2173, 2281, 2395, 2514} is not geometric, but it's somewhat close to it.

Answer by josgarithmetic(39617)   (Show Source):
You can put this solution on YOUR website!
first ratio 1.0497
second ratio 1.04998
third ratio 1.04969

None completely in agreement.
Try taking as ratio being 1.050 and see what happens.

first term 2173
and then 2281, 2395, 2515
but terms 2, 3, and 4 were truncated for the whole number part.