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Mathematics: Post your doubts here!

GetSomeLife

GetSomeLife

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anooshraja said:
QUESTION iv and v​
partbii,iii,iv and v​
plz for sake of ALLAH TANKYOU​
Click to expand...
a)
i) 1 + 2 + 3 + 4 = 10
ii) n=3
n(n+1)/2
3(3+1)/2
12/2
=6
iii) 120(120+1)/2
120*121/2
= 7260
iv) n = 200
[n(n+1)/2] - [7260] We write 7260 because notice that they have started the sequence from 121. So, we have to EXCLUDE the sum of the first 12o integers
200*201/2 - 7260
= 12840
v) Even numbers = multiples of '2'
Instead of n+1, we'll use n+2
PLUS we'll divide it by 2 to remove sums of odd numbers :)

n(n+2)/2 * (1/2)

Put 800 in place of n and you'll get your answer

b)
i) Use you'r calculator!
ii) Notice that:

Integer sum = 1, Cube sum = 1
Integer sum = 3, Cube sum = 9
Integer sum = 6, Cube sum = 36

So, integer sum SQUARE is cube sum!

integer sum = 105, Cube sum = 105^2 = 11025
iii)
Integer Sum = n(n+1)/2
So, Cube sum = [n(n+1)/2]^2
iv)
n = 60
Put in place of n.
Ans = 3348900
v)
[n(n+1)/2]^2 = 278784

Find n :)
 
sma786

sma786

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Lost_Life said:
well, the nth term can be found using the formula An+_b
Where A is the difference in the numbers
example:
5,7,9,11..etc..
to find the A, you subtract the numbers to get a COMMON difference
that difference is A; in this case 2 (7-5),(9-7),..
Next, B, is how much to get to the first number of the sequence
that means how much 2 has to get to 5, which is 3
so the nth term(formula) is 2n+3
hope that helped
Click to expand...
Thanks ! but thats for sequences with constant difference .. what for 1, 2, 4, 8, 16 .. ??
 
beewhiz997

beewhiz997

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sma786 said:
Thanks ! but thats for sequences with constant difference .. what for 1, 2, 4, 8, 16 .. ??
Click to expand...
some tips
3^2, 5^2, 7^2 = 2n+1

0^3, 3^3, 6^3, 9^3 = 3n-3

so the difference is constant. for these, take the power, and then add or subtract accordingly.
e.g the 1st example the power is two. so put 2n. then, what do you add or subtract from 2n to get the term? in this case its 1.

1^3,4^5, 9^7 = n^2

3^3, 6^5, 11^7, 18^9

so the difference increases by constant here. for these initially put n^2. then whatever you add or subtract to get the term add it to the n^2 as above.

2^2, 4^4, 8^8

1^2, 3^4, 7^8

so the difference is doubling so put 2^n. then same as above.

if difference triples... put n^3

hope i helped!
 
shafayat

shafayat

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amirjalili said:
Hi guys
i have a very technical question.
what is an exact value ?

like in the question no.1 , wat should be the answer ?
is it 4.50 x 10^9 or 4.496 x 10^9
i checked the marking scheme , it says its 4.496 x 10^9 but shuldnt we round this off to 3s.f ???
Click to expand...
we shud round off but when it says exact ... it means what is shown in calculator ... so write whatever calcu says
 
sma786

sma786

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beewhiz997 said:
some tips
3^2, 5^2, 7^2 = 2n+1

0^3, 3^3, 6^3, 9^3 = 3n-3

so the difference is constant. for these, take the power, and then add or subtract accordingly.
e.g the 1st example the power is two. so put 2n. then, what do you add or subtract from 2n to get the term? in this case its 1.

1^3,4^5, 9^7 = n^2

3^3, 6^5, 11^7, 18^9

so the difference increases by constant here. for these initially put n^2. then whatever you add or subtract to get the term add it to the n^2 as above.

2^2, 4^4, 8^8

1^2, 3^4, 7^8

so the difference is doubling so put 2^n. then same as above.

if difference triples... put n^3

hope i helped!
Click to expand...
thanks alot =]
 
B

bluefa1con

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btw what do u guys suggest
should we round off the probability?
in some marks scheme the answer is given in full form while in other its rounded off
 
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