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Mohit_C

How do you find the number of terms in the following geometric sequence,

729, -243, 81....-1/3

Pls explain,

thanks

729, -243, 81....-1/3

Pls explain,

thanks

Let the first term be 'a', the common ratio be 'r', and the number of terms be 'n'.

a = 729

r = -1/3

The last term = ar

-1/3 = 729*(-1/3)

-1/2187 = (-1/3)

Solving this gives n = 8.

Therefore, there are 8 terms in the sequence ...

Hope this helps,

~~Simba

consider what is happening with each term;

first term to second term occurs through division by -3, the same generates the next term

=> the common ratio = -1/3

we need to find when ar^{n} = -1/3

Using a=729

=> r^{n} = -1/2187

this is the same as (-1/3)^{7}

=> sequence goes from ar^{0} -> ar^{7} , and so contains 8 terms

first term to second term occurs through division by -3, the same generates the next term

=> the common ratio = -1/3

we need to find when ar

Using a=729

=> r

this is the same as (-1/3)

=> sequence goes from ar

Mohit_C

I dont get this, how do you get rid of the - and get a positive number. Pls explain.

after multiplying by -1

-1 * -1/2187 = -1 * (-1)

the left hand side becomes positive, therefore the right hand side must also be positive:

-1 * (-1)

now 3

so -1 * (-1)

Ok i got another one here:

C2 Examination style:

A father promises his daughter an eternal gift on her birthday. On day 1 she receives €75 and each following day she receives 2/3 of the amount given to her the day before. The father promises that this will go on for ever. After k days the total amount of money that the daughter will have received exceeds €200. c) Find the smallest value of k.

Thanks.

C2 Examination style:

A father promises his daughter an eternal gift on her birthday. On day 1 she receives €75 and each following day she receives 2/3 of the amount given to her the day before. The father promises that this will go on for ever. After k days the total amount of money that the daughter will have received exceeds €200. c) Find the smallest value of k.

Thanks.

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