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Please help with this question!

If the sum of first 100 terms of a GP is 0 and the first term is -1, then the common ratio of GP will be:
i)2
ii)1
iii) -1
iv)1
I generally think that the answer should be 1 but the actual answer is -1. So I tried the whole formula for the sum of the no. of terms of GP and I'm still getting 1. Please help.
Original post by a_09
If the sum of first 100 terms of a GP is 0 and the first term is -1, then the common ratio of GP will be:
i)2
ii)1
iii) -1
iv)1
I generally think that the answer should be 1 but the actual answer is -1. So I tried the whole formula for the sum of the no. of terms of GP and I'm still getting 1. Please help.


It can’t be 1 otherwise it wouldnt go to 0.

You’d basically just be left with -1 -1 -1 + ... -1 = 0 which is not possible
Reply 2
Avatar for a_09
a_09
OP
8
Original post by RDKGames
It can’t be 1 otherwise it wouldnt go to 0.

You’d basically just be left with -1 -1 -1 + ... -1 = 0 which is not possible


Can you please show me some working.
Reply 3
Avatar for Notnek
Notnek
21
Original post by a_09
If the sum of first 100 terms of a GP is 0 and the first term is -1, then the common ratio of GP will be:
i)2
ii)1
iii) -1
iv)1
I generally think that the answer should be 1 but the actual answer is -1. So I tried the whole formula for the sum of the no. of terms of GP and I'm still getting 1. Please help.

Try summing the first say 6 terms of a sequence with a = -1 and r = -1 and you should notice something. Then compare this with a series with a = -1 and r = 1 (RDKGames has already shown why this won't give you a sum of 0).

If you're using the sum formula then that might produce two answers but remember that you can't divide by 0...

Please post all your working if you're still stuck.
Reply 4
Avatar for a_09
a_09
OP
8
Original post by Notnek
Try summing the first say 6 terms of a sequence with a = -1 and r = -1 and you should notice something. Then compare this with a series with a = -1 and r = 1 (RDKGames has already shown why this won't give you a sum of 0).

If you're using the sum formula then that might produce two answers but remember that you can't divide by 0...

Please post all your working if you're still stuck.

Here's the working as per the sum formula(I hope I'm not doing it the wrong way) :-
S(100)=(a(r^n)-1)/r-1
0=(-1(r^100)-1)/r-1
0=(r^100)-1
r^100=1
r=1
I get your point, that multiplying it with -1 would result in -1,1,-1,.... and thus the sum will be 0.
Reply 5
Avatar for Notnek
Notnek
21
Original post by a_09
Here's the working as per the sum formula(I hope I'm not doing it the wrong way) :-
S(100)=(a(r^n)-1)/r-1
0=(-1(r^100)-1)/r-1
0=(r^100)-1
r^100=1
r=1
I get your point, that multiplying it with -1 would result in -1,1,-1,.... and thus the sum will be 0.

r^100 = 1 has two real solutions. What are they?

r = 1 is invalid as I said in my last post because that would mean that s(100) has a 0 on the denominator which is not possible.

When you solve a fraction equal to 0, you are right to set the numerator equal to 0 but you always should check to see if your solutions are valid.
Reply 6
Avatar for a_09
a_09
OP
8
Okay. Yeah, got it. Thank you! 😃

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