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please answer this nth term question! if you know!

there are 64 squares on a grid. work out how many grains of rice there are ALTOGETHER in the grid if the first box contains 1grain, the second box contains 2 grains and the third box contains 4 grains. work out the formula to help.

I would be very grateful if you could explain it in an easy way!
Reply 1
Avatar for ThomH97
ThomH97
21
I'm assuming you know how to write how many grains of rice there will be on the n-th square?

Since it's asking you for the total after 64 squares, can you write the sequence for how many there are in total after n squares? So we have 1, 3, 7, ...
This is a geometric series question, you have to use the equation Sn = a(r^n - 1)/(r-1)

where a is the number of rice in the first box, r is the common ratio ( so in this case it is 2), and n is the number of boxes ( so 64). Sn is the total number of rice.
Original post by cool_cool
there are 64 squares on a grid. work out how many grains of rice there are ALTOGETHER in the grid if the first box contains 1grain, the second box contains 2 grains and the third box contains 4 grains. work out the formula to help.

I would be very grateful if you could explain it in an easy way!

Like James said before, it's a geometric series (multiplying by two for each term). The formula is as he said: Sn = a(r^n - 1)/(r-1).

I'll elaborate a little more - 'Sn' means the sum of n terms, so S64 = a(r^64 - 1)/(r-1). 'a' is the first term in the series, so 1 in this case. 'r' is the common ration, i.e. what the series multiplies each item by to receive the subsequent term, i.e. 2 here.
Reply 4
Avatar for cool_cool
cool_cool
OP
14
Original post by JJJJJAAAAMES
This is a geometric series question, you have to use the equation Sn = a(r^n - 1)/(r-1)

where a is the number of rice in the first box, r is the common ratio ( so in this case it is 2), and n is the number of boxes ( so 64). Sn is the total number of rice.


ok thank you. although I was told that the equation was: 2^n-1 + 2^n-1 -1
i find it useful to write out the results in a table and then try to find a pattern

In this case we have

Squares : 1 , 2 , 3 , 4 , 5 , ...
Grains : 1 , 3 , 7 , 15 , 31 , ...

If we compare the (grains) with 2^(squares) we see a pattern

So I have (grains) = 2^(squares) - 1
Reply 6
Avatar for cool_cool
cool_cool
OP
14
thank you! that makes sense.
Original post by begbie68
i find it useful to write out the results in a table and then try to find a pattern

In this case we have

Squares : 1 , 2 , 3 , 4 , 5 , ...
Grains : 1 , 3 , 7 , 15 , 31 , ...

If we compare the (grains) with 2^(squares) we see a pattern

So I have (grains) = 2^(squares) - 1

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