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# Simple Geometric series Question Help watch

1. Thanks:

Find the number of terms in this geometric series

8/81 -4/27 + 2/9......-1 11/16 ( thats meant to be -1 and 11/16)

You cant use logs this time so how do you do it. I just can't thinK!
2. (Original post by MAC1205)
Thanks:

Find the number of terms in this geometric series

8/81 -4/27 + 2/9......-1 11/16 ( thats meant to be -1 and 11/16)

You cant use logs this time so how do you do it. I just can't thinK!
The common ratio is -3/2

The kth term is 8/81 (-3/2)^(k-1)

So you're looking to solve

8/81 (-3/2)^(n-1) = -1 11/16 = - 27/16

So

(-3/2)^(n-1) = - (81 x 27)/(16 x 8) = -(3/2)^7

So n-1 = 7

So n = 8
3. So

(-3/2)^(n-1) = - (81 x 27)/(16 x 8) = -(3/2)^7

Got up to this bit. But how would you know that -(3/2)^7 without using logs or trial and error?
4. - (81 x 27)/(16 x 8) = - (9² x 3³)/ (4² x 2³)
= - [ (3²)² x 3³ ] / [ (2²)² x 2³ ]
= - [ 34 x 3³] / [24 x 2³]
= - 37/27 = -(3/2)7

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