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Please help tq
Date Posted: 5 years ago
Views: 468
From 9 am to 11 am, 2 hours have passed.
2 hours = 120 min
120 min ÷ 15 min = 8
There are eight 15-min periods.
So the rumour passing started by the 4 villagers was done over 8 periods.
First 15 min, each of the 4 villagers told another 3 unique villagers. Then all of them each told another 3 unique villagers. So on and so forth.
Number of people who were told the rumour :
Before 9.00 am : 4
9.00 am to 9.15 am (first period) :
4 x 3 = 12
9.15 am to 9.30 am :
12 x 3 = 4 x 3 x 3 = 4 x 3^2
= 36
9.30 am to 9.45 am :
36 x 3 = 4 x 3^2 x 3
= 4 x 3^3 = 108
.
.
.
10.45 am to 11.00 am (8th period) :
4 x 3^8 = 26244
Realise that this works out to be a GP, with first term 4 and common ratio 3. Number of terms is 9.
So you can just use your formula for sum of GP.
S9
= 4(1 - 3^9) ÷ (1 - 3)
= 39364
2 hours = 120 min
120 min ÷ 15 min = 8
There are eight 15-min periods.
So the rumour passing started by the 4 villagers was done over 8 periods.
First 15 min, each of the 4 villagers told another 3 unique villagers. Then all of them each told another 3 unique villagers. So on and so forth.
Number of people who were told the rumour :
Before 9.00 am : 4
9.00 am to 9.15 am (first period) :
4 x 3 = 12
9.15 am to 9.30 am :
12 x 3 = 4 x 3 x 3 = 4 x 3^2
= 36
9.30 am to 9.45 am :
36 x 3 = 4 x 3^2 x 3
= 4 x 3^3 = 108
.
.
.
10.45 am to 11.00 am (8th period) :
4 x 3^8 = 26244
Realise that this works out to be a GP, with first term 4 and common ratio 3. Number of terms is 9.
So you can just use your formula for sum of GP.
S9
= 4(1 - 3^9) ÷ (1 - 3)
= 39364
See 1 Answer
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hope this helps! (:
Date Posted:
5 years ago
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