Geometric series (1 Viewer)

[reggie7]

Could someone please explain how to answer these tricky questions:

1) Which term of the series 8 - 4 + 2 - .... is equal to 1/128 ?

2) Which term of the series 3 + 21 + 147 + .... is equal to 352,947 ?

3) Which term of 7/9 + 14/45 + 28/225 + ... is equal to 224/28,125 ?

4) The third term of a geometric series is 2/5 and the 5th term is 1r 3/5. Find the common ratio and the first term,

5) Find the first term of the series 2/7 + 6/7 + 2r 4/7 + ... that is greater than 100.

The 1st question my teacher couldn't even explain..

Answers:
1) 11th
2) 7th
3) 6th
4) a = 1/10, r = +- 2
5) 208r 2/7 (7th term)

Just need explainations thanks.

 

[reggie7]

Then it's really just the same process for 2 and 3, find r, find the nth term, let Tn = the number your given, put them both to the same base and equate the powers.

Does that make sence??

With Q. 2 and Q. 3 I believe you need to use logs? Could you please explain how to do that?

 

[Air Jordan]

2) 3 + 21 + 147 + .... r= 7

=a

352947 = 3 x

117649 =



n - 1 = 6

n = 7

 

[Air Jordan]

3) 7/9 + 14/45 + 28/225 + ...



























n - 1 = 5



n = 6